2017-2018 Problem of the Week (POTW) #1 - POTW Math Enrichment!
Welcome New and Old Cranny Intermediates! It's POTW time again!
Welcome back all returning Cranny Intermediates, and hello to all of you new Intermediates! (i.e. Grade 7s and newcomers to our school).
As most of you know, this website is a space where Mr. Milette seeks to challenge you with the Math Problem of the Week! (A.K.A. POTW). Two questions will be posted each week. One question is geared toward the Grade 7s and a second question is more for the Grade 8s. You are challenged to answer both questions each week, but only your specific-grade question is mandatory. Both of the Grade 7 & 8 questions can be considered enrichment-type math problems, so they’re a great way to be challenged!
The most important requirement of this website is YOUR participation. This may come in the form of:
- sharing your POTW answer
- posting your comments, questions, and replies to others
- seeking out the answers to POTWs (answers are posted a week after the question has been posted)
- reading and following new posts
With that being said, it is absolutely pivotal that you remind yourself about online netiquette. You must always consider the feelings of others when posting comments. Before you press 'submit' or 'send' or 'publish' please ask yourself two questions: "Would I say this in-person to someone's face?" and "Is my comment helpful?" If the answer to either of those questions is "No" then consider revising your comment.
You will find below the first POTW for the 2017-2018 school year! Please submit any and all responses regardless if you think someone else has the same answer. Both Grade 7 and Grade 8 students can submit answers in the same reply section, please just state which question you’ll be answering at the beginning of your post. You can always show your work in different ways! And be sure to comment on other students' work, provide feedback, and ask clarifying questions.
Always remember to be signed-in to your gapps account before submitting a response. Enjoy the POTW!
Grade 7 POTW #1
Esther had a sweet summer job, working at the Maple Community Centre. Her job was to make sure the company’s employees are being paid relatively equally based on their responsibilities. She needs to review all employee records by location: the pool, library, fitness area, etc. The pool manager, Jessica, volunteers to go first, while its longest serving employee, David, decides to go second. Esther surveyed the salaries of all the pool staff and finds the following annual salaries:
$35,000, $42,000, $36,000, $74,000, $38,000, $40,000, $39,000, $42,000
What is mean salary of the Maple pool? What is the median? The mode? What is the range of the salary? Which salary is probably Jessica’s salary? Why do you think that?
Grade 8 POTW #1
The chart above shows the gas
prices in the GTA for the past month. For each of the past 4 Sundays the prices
were (in cents/Litre):
109.8, 109.3, 111.1, 129.7
What was the mean gasoline Sunday
price? What was the median Sunday price? The mode? Which measure of central
tendency is most accurate to represent this particular data set? Are there
outliers? If so provide SEVERAL REAL-WORLD explanations for the outlier(s)? Is
there a trend in the data set? If so provide SEVERAL REAL-WORLD explanations
(you may need to research).
For the mean you add all the integers then divide the sum by the number of integers.
ReplyDelete$35000+$42000+$36000+$74000+$38000+$40000+$39000+$42000=$346000
$346000 divided by 8=$43250
Mean=$43250
For the median you order the numbers from least to greatest and then find the middle number. If there are 2 middle numbers, you find the mean of them or add them and then divide that by 2.
$35000,$36000,$38000,$39000,$40000,$42000,$32000,$74000
$39000,$40000 are the middle numbers
$39000+$40000=$79000 divided by 2=$39500
Median=$39500
The mode is the number that appears the most. There can be multiple modes.
$35000, $42000, $36000, $74000, $38000, $40000, $39000, $42000
42000 is the only value that appears twice or more.
Mode=$42000
Jessica's salary is most likely $74000. I know this because firstly, the manager usually gets the most money in the real world and $74000 is the highest pay. Secondly, the salary is almost double the other salaries. There isn't another pool job that can possibly earn that much other than a manager. It also makes no sense for a pool worker to get double the pay of other pool workers that all do the same jobs as well as getting more pay than the manager.
-Seayrohn
Sorry about forgetting the range.
DeleteThe range of a set of data is the difference between the largest value and the smallest value.
74000 - 35000 = 39000
Range=39000
Once again sorry I forgot about that.
sorry i forgot to say that my first post was grade 7 POTW
ReplyDeleteGrade 8 POTW
ReplyDeleteThe mean is when you add all the integers and the divide the sum by the number of integers.
109.8 + 109.3 + 111.1 + 129.7= 114.975
Mean=114.975
The median is the middle number of integers when ordered from least to greatest. If there are two middle numbers, then the median is the mean of those two integers.
109.3, 109.8, 111.1, 129.7
109.8+111.1=220.9 divided by 2=110.45
Median=110.45
Mode is the integer that appears the most. There can be multiple modes based on the data set. However, if there isn't any number that appears more than another than there is no mode.
109.8, 109.3, 111.1, 129.7
No number appears more than another so there is no mode.
The mean is the most accurate central tendency to represent the data set. The mean is because the mode represents nothing, the median just shows the middle of the values which isn't accurate because let's say the values were 1,2,3,123 the median will not show the overall average. It seems like the average with the data set will be somewhere in the middle of 1 to 100 but is just 2.5 for the median. The mean is great because it takes everything and averages it up.
(I just learned what outliers are) Yes there are a few outliers. From the last Friday to the last Monday, there were outliers. Before that every day costed around 109.3 cents. Then it suddenly branched up all the way to 129.9 cents. I believe an outlier could have been caused here due to the weather. In October everything was around 109.3 cents. Then at the end of October and beginning of November it went up. It could have been because Toronto is a busy place and the gas station would want as much money possible. When weather starts to become colder and below 0 degrees, freezing rain snow, etc will slow them down. This November could've been really cold and had that traffic. In traffic you waste gas a lot so the gas station will be commonly used. Therefore, they raise the price knowing it gains more money.
The trend in this graph and time is an upward trend. It could be because of the same reason as the outliers, but I'll give another one. In November, people started to come and visit the place. Toronto already is a busy place but more business just makes lots of traffic. Like before, the gas price will be raised more for those who wasted their gas in traffic.
But look closely at the graph, the data is for August (summer).
DeleteOh...
DeleteFor some reason I thought 8 months is October.
I made a mistake before.
DeleteYou explained in class about school marks and how they use median instead of the mean.
This situation is just like that. So the median will be the most accurate to represent the data because the outlier will throw off the mean and the mode doesn't make sense. There is no mode and even if there is, it doesn't change too much unless there was no outlier and everything was close to each other.
I would say my re-answer for the reason behind the outlier and trend, but I already saw the other comments and I already know the answer is Hurricane Harvey
DeleteExcellent understanding of the median vs. mean usage for central tendency.
DeleteOk, so I guess that I'll do the grade 8 POTW first since it's the one that I'm required to do.
ReplyDeleteSo figuring out the mean is easy: You just add up the four values and divide it by 4, since that's the number of values.
(109.8+109.3+111.1+129.7)/4 = 459.9/4 = 114.975
Overall, the mean is 114.975.
There is no mode in this set because none of the numbers repeat itself, so let's get onto the median.
Ordering the values, I get 109.3, 109.8, 111.1, 129.7.
Since the number of Sundays is an even number, I will have to average out the two middle numbers, 109.8 and 111.1. This gives me 110.45.
The measure of central tendency would be the median because it shows the middle number, excepting outliers. There is an outlier in the set because there is one price that is very high, above all others, which is 129.7(I'm guessing because of hurricane Harvey?). There is a growing trend in the data set. This is probably because(From what I read on the news) hurricane Harvey causing so much havoc in Texas, it made one quarter of the oil offline, so the other places keep growing in price to compensate for the lost amount.
Your "guess" was spot-on Alan!
DeleteGrade 7 POTW(I guess I'll do it like the old times...):
ReplyDeleteThe mean is adding all the values up and finding the average, so I add them up and divide by 8 since 8 is the number of terms.
This averages to $43250. Therefore, the mean is $43250.
I can order the numbers so that the order is 35000, 36000, 38000, 39000, 40000, 42000, 42000, and 74000.
The median would then be the mean of the two middle numbers, 39000 and 40000. These average out to be 39500. The median is thus, $39500.
Since there is a repeat of 42000, this makes $42000 the mode of the salaries.
The range would be the largest value minus the smallest value, which would be:
74000 - 35000 = $39000.
I would guess that Jessica's salary is $74000 since she is the pool manager so she probably earns more than everyone else.
ogalyboogalyboo
ReplyDeleteMean=114.975
ReplyDelete109.8+109.3+111.1+129.7 459.9
----------------------------------- = ------------- =114.975
4 4
Median=110.45
109.3,109.8,111.1,129.7
1 2 3 4
109.8+111.1
109.8,111.1= --------------------- =110.45
2 3 2
Mode= this data has no mode
The outlier is clearly 129.7 because it is more than 10 cents above the previous number which might not sound like much but in this context is a lot. I don't know why the gas rose in this exact scenario but according to national resources canada the reasons may be.
Temporary closures while refineries install new equipment or conduct maintenance ( which means the company must build a new machine or repair an old one so they raise the prices to make sure they get the same money as they would in that time well they cans supply gas)
The high cost of construction (meaning that they are building a new supply arya so that means pay for construction, for people to work there and, ECT. so they need mot money)
But the most likely reason is they want dola dola billz yall
testing testing
ReplyDeleteThis is a comment.
ReplyDeleteBloop Bleep berbity berp berpp does this work
For the gr.8 potw the mean is 114.975, the median is 110.45 and there is no mode. The most accurate one is the median because in this data set there is an outlier (129.7) so that messes up the mean but doesn't affect the median. Why that might be is a oil shortage or the oil plants could be injured. A trend is that the oil prices remain relatively the same up until Oct. 30th when the prices start to skyrocket. This could be the cause of finding a cheaper gas substitute to be distributed so the prices start to lower and then inflation starts to hit the prices and then something happened and the prices started to skyrocket.
ReplyDeleteThe month shown is August though?
Deletefor grade 7 potw the mean is 43,250, median 39,500, mode 42,000, and range 39,000
ReplyDeletei found the mean by adding up all of the numbers which got a sum of 346 then divided by how many integers there were which was 8
i found median by lining the integers smallest to biggest and found the middle
for mode i counted that there was 42,000 repeated twice
and for range i found the differnece between the smallest number and the biggest number which was 74,000 and 35,000
and the final question which salary do you think Jessica's was, i couldn't quite get an answer because i couldn't get any information about Jessica but i do know that David's salary is probably 74,000 because they did mention that he worked at maple for the longest(just an assumption)
But, in the question it says the Jessica is the manager. Wouldn't that be reason for a higher salary?
Deletesorry i didn't see that part, i thought they were all employees, opps
DeleteGrade 8 POTW
ReplyDeleteTo find the mean, I added all of the prices together and divided by 4 (total number of values) to get 114.975. To find the mode, I placed all of them in order from least to greatest, and since there was an even number of values, found the mean of the two middle values which was 110.45. Since none of the values were the same, there is no mode. One outlier is that on August 29th, prices started to go up. This corresponds with the rise in the Canadian Dollar's value (2 days), which could be because of the Bank of Canada's interest rate hike. Two real world examples of this are when the Brexit results came in and the Euro dropped, and when a certain someone got elected and the stock market reached an all-time high.
Dhruv, the Bank of Canada's recent interest rate hike (frowny face) will impact mortgage rates, lending rates, credit card fees, amongst other things, but it WON'T really impact gasoline prices in the way shown in the data.
Deletefor grade 8 potw the mode was 114.975 which i found by adding the numbers then dividing them by how many numbers there were. the median is 110.45 which is found by lining the numbers smallest to biggest then finding the middle, this case I had to find the mean of 109.8 and 111.1. yes there is an outlier which is 129.7 because it is way off from the other three numbers. the most accurate central tendency is median because the mean is thrown off by the outlier. real life application could be gas prices going up for all gas stations. a trend i noticed was that the prices of the gas was pretty normal/stable then all of a sudden it went up in a short amount of time. real life application is that supply and demand of crude oil would make gas prices go up because majority of gasoline is made up of crude oil
ReplyDeleteGrade 8 POTW:
ReplyDelete109.8, 109.3, 111.1, 129.7
The mean of the the four sundays is 114.975, the median is 110.45 and there is no mode. I believe the central tendency I would use is median because 129.7 is pretty high for gasoline. I think the gas prices are going up because on Global news, I saw it said "Hurricane Harvey driving up gas prices"(or something along the lines of that also see the pun?) And there is an upward trend since it gets higher. Another reason why the gas price might be up is because perhaps workers are on strike or a lawsuit against workers who die on the job.
Grade 7 POTW:
$35,000, $36,000, $38,000, $39,000, $40,000, $42,000, $42,000, $74,000
Mean:43,350
Median: 39,500
Mode:42,000
Range:39,000
I think Jessica's salary is 74, 000 because she is a pool manager and from what I researched, a pool manager can have a pretty high salary. $23 dollars an hour, the average american works for 8.8 hours and so if we do the math, that's around 73 000. Of course she is a manager and general managers make around $18-$23 dollars an hour.
Excellent Hurricane Harvey connection Cindy.
DeleteFor Grade 7 POTW:
ReplyDeleteMean: Mean is bassically the average of all the values or data that you have.
$35,000+$42,000+$36,000+$74,000+$38,000+$40,000+$39,000+$42,000=$346,000
346,000/8= 43,250
-The mean of all the sallaries is $43,250
Median: median is when you order all the numbers from smallest to largest, the middle number is the median.
Ordering the numbers: $35,000, $36,000,$38,000,$39,000,$40,000,$42,000,$42,000, $74,000
-There are two numbers in the middle: 39,000 and 40,000 - so we have to find their average. their average will be the median.
39,000+40,000=79,000
79,000/2=39,500
so, the median of the salaries is $39,500.
Mode: the mode is the number that appears most in the set of values.
$35,000, $42,000, $36,000, $74,000, $38,000, $40,000, $39,000, $42,000
in this case the mode would be $42,000 since it is the only number that comes up twice, and the only number that appears more than once.
I think that Jessica's salary is probably the largest: $74,000- I think this because since Jessica is a pool manager she does the most work, she has to organize the equipment supervise and do countless other tasks. Jessica should be payed for her work so I think the $74,000 is hers.
Grade 8 POTW (woohoo)
ReplyDeleteGasoline Sunday Mean Price: 114.975
109.8 + 109.3 + 111.1 + 129.7 = 459.9
459.9 / 4 = 114.975
This was calculated by adding all the prices together, then dividing the sum by the amount of numbers that were given.
Gasoline Sunday Median Price: 110.45
109.3, 109.8, 111.1, 129.7
(109.3 + 111.1) / 2 = 110.45
This was solved by first ordering all the numbers in order, from least to greatest. Then, the number in the middle was identified. Though in the set of numbers, there is no middle (or there are 2 numbers in the middle). You then find the middle of the 2 numbers in the middle.
Gasoline Sunday Mode: None
There are no repeating numbers in this set of data, therefore, there is no mode.
I believe that the most accurate measure of central tendency is the median. In this set of data, there is an outlier, 129.7. An outlier tends to modify the mean because there is a large gap between the general area in which most of the numbers are and the outlier. A reason for the outlier may be because of a sudden high demand in another country for gas/oil. I have heard that adjustments from "summer-blended gasoline" to "winter-blended gasoline" can cause sudden changes to gas prices.
There is a growing trend in the data as well. It is not so noticeable at first, but during August 23 and August 28, you start to see the prices rising quickly. It may also be because of the previous reason(s).
Very clear work Ella.
DeleteFor Grade 7 POTW:
ReplyDeleteMean: Mean is bassically the average of all the values or data that you have.
$35,000+$42,000+$36,000+$74,000+$38,000+$40,000+$39,000+$42,000=$346,000
346,000/8= 43,250
-The mean of all the sallaries is $43,250
Median: median is when you order all the numbers from smallest to largest, the middle number is the median.
Ordering the numbers: $35,000, $36,000,$38,000,$39,000,$40,000,$42,000,$42,000, $74,000
-There are two numbers in the middle: 39,000 and 40,000 - so we have to find their average. their average will be the median.
39,000+40,000=79,000
79,000/2=39,500
so, the median of the salaries is $39,500.
Mode: the mode is the number that appears most in the set of values.
$35,000, $42,000, $36,000, $74,000, $38,000, $40,000, $39,000, $42,000
in this case the mode would be $42,000 since it is the only number that comes up twice, and the only number that appears more than once.
I think that Jessica's salary is probably the largest: $74,000- I think this because since Jessica is a pool manager she does the most work, she has to organize the equipment supervise and do countless other tasks. Jessica should be payed for her work so I think the $74,000 is hers.
testing, this is a weird font when you type
ReplyDeletetesting
ReplyDeleteGrade 7 POTW:
ReplyDeleteMean: To find the mean/average of the set, I added up all the numbers together, then divided by the number of numbers there are. 35000+42000+36000+74000+38000+40000+39000+42000= 346000
346000/8=43250. The mean is 43250.
Mode: Every number was not repeated except for 42,000. The mode is 42000.
Median: I first lined up the numbers from smallest to largest. Since there were an even number of numbers in this set, I took the middle two, and found the mean/average of them.40000+39000=79000 79000/2= 39500. The median is 39500.
Range: To find range, you take the biggest and smallest numbers and you find the difference between them. 74000- 35000=39000. The range is 39000.
For the last question about Jessica's salary, I was a little confused. I assume David's salary would be the most (74000) since he had worked at the centre for the longest time. That may not be true.
Management tends to earn more than employees though?
DeleteGrade 7 POTW
ReplyDeleteMean is another word for average, which you find by adding up all the numbers and then dividing, by the number of those numbers. This will result in the mean, which in this case is 43,250.
Next is median. I found out the median by placing all the integers in order from smallest to largest. The two ones in the middle were then added and divided to find the mean of both numbers, which then results in the median, in this case, 39,500.
Mode is easier; it's simply the finding of the most repeated numbers, in this case, it's 42,000, which is repeated twice.
Range is the difference between the largest and smallest numbers, which is 35,000 and 74,000. The difference between the two is 39,000, which is therefore the range.
The final question was more difficult for me, as I couldn't pinpoint how Jessica would be paid exactly, but I guessed that it would probably be less than David's, who would probably receive the highest pay as he worked the longest. My guess is that then Jessica would probably be paid second-most, 42,000, as caring for a pool is a lot of work, but not enough to guarantee 74,000, which is a high level of pay.
Yes, that last part was not cut-and-dry, you needed to infer.
DeleteGRADE 7 POTW:
ReplyDeleteMean - All numbers added up and divided by the amount of numbers in the sequence
35,000 + 42,000 + 36,000 + 74,000 + 38,000 + 40,000 + 39,000 + 42,000 = 346,000
There are eight numbers in this sequence.
346,000 / 8 = 43,250
Median - The "middle" number
I placed all the numbers in order of least to greatest:
35,000, 36,000, 38,000, 39,000, 40,000, 42,000, 42,000, 74,000
There happens to be 2 numbers in the middle: 39,000 and 42,000, so I found the average of the two numbers, which was the median. (39,000 + 42,000) / 2 = 40,500.
Mode - Number that appears the most
There is a repeat of 42,000, so that mode.
Range - Greatest number subtracted by the smallest number
Greatest number: 74,000
Smallest number: 35,000
74,000 - 35,000 = 39,000
And for Jessica's salary, it only tells us that Jessica is the pool manager, which isn't enough for us to figure out what her salary is. Because of the lack of information, I'm just going to assume that her salary is close to the average (43,250) because I think it's a slightly safer approach then just guessing what a pool manager's salary would be.
Oh sorry I accidentally did the median wrong. The two middle numbers were 39,000 and 40,000, not 42,000.
Delete(39,000 + 40,000) / 2 = 39,500
39,500 is the correct median
This comment has been removed by the author.
ReplyDeleteGrade 8:
ReplyDeleteTo find the mean of a set of data, the values being used should be added, then divided by the number of integers in which the mean is being established. In this scenario, with the gas prices for the past 4 Sundays being 109.8 cents per litre, 109.3 cents per litre, 111.1 cents per litre, and 129.7 cents per litre, these four values should be added, giving the value of 459.9 cents per litre. As for there being 4 integers in which the mean is being found, 459.9 should be divided by 4, establishing the value of 114.975, which can be rounded to 115 cents per litre.
The median of a set of data is the value essentially in "the middle" when laid out in order from least to greatest. If the number of integers is even, the 2 numbers in the middle's mean's should be found to perceive the median of the entire set of data. 109.8, 109.3, 111.1, and 129.7 when laid out in order are 109.3, 109.8, 111.1, and 129.7, leaving both 109.8 and 111.1 in the middle. 111.1 + 109.8 = 220.9, which when divided by 2 gives the value of 110.45, that of which can be rounded to 110.5.
The mode of a set of data is the value that appears the most within the group of numbers. In the scenario of no values repeating themselves, which is the case with this set of data, there is no mode, thus there isn't a mode in this situation; although, if there are multiple values repeating by the same number of times, there can be multiple modes.
Furthermore, when there's an outlier in a set of data, the median most often represents the most accurate representation as a central tendency. Although 129.7 cents per litre is far more than the prices from the 3 Sundays before it, gas prices are consistently changing at different rates. Considering this, 129.7 could possibly not be seen as an outlier, making the mean the most accurate representation of the average.
In the specific graph shown there is a trend of the gas prices in Toronto gradually increasing, which can be further clearly seen throughout the most recent week shown, with the gas price increasing by a higher rate. Having seen the extended version of the graph with 11 years, there are many times in which the prices have went both higher and lower, essentially ending with the price being higher than it was 11 years ago, giving the assumption in which the trend is gas prices are progressively increasing, in which there could be many factors influencing it in such a way. Such factors include natural disasters, including hurricane Harvey, which caused gas prices to increase at the end of August.
Grade seven POTW:
ReplyDelete1.
The mean determines the average of a group of numbers.
To find the mean, I simply added up all of the salaries and divided outcome by the number of salaries in total listed:
$35,000 + $42,000 + $36,000 + $74,000 + $38,000 + $40,000 + $39,000 + $42,000
= $346,000
There are 8 salaries in total
$346,000/8
= 43,250
Mean = 43,250
2.
The medium is the number in the middle if you put the numbers in order.
To find the medium, I put the salaries in order (smallest to largest):
$35,000, $36,000, $38,000, $39,000, $40,000, $42,000, $42,000, $74,000
In that order, the middle numbers were $39,000 and $40,000
To find the real medium, you have to find the mean between them which was $39,500
Medium: $39,500
3. The mode is the most repeated number in sequence
Finding the mode is simple, It's the most repeated number in the sequence.
$42,000 is repeated twice which makes it the mode since none of the other numbers are repeated in that sequence.
Mode: $42,000
4. The range is the difference between the biggest number and the smallest number.
To find the range, you simply subtract the biggest number (In this case, it's 74,000) and the smallest number (It's 35,000)
$74,000 - $35,000
= $39,000
Range = $39,000
5. I think Jessica's salary should be $74,000 because management is a very important job to have in general. Without a manager, the business/community center would be very disorganized. Even though David has worked at the community center longer, Jessica's role is more vital to the community center. But this all mainly depends on what job David has.
Maxwell's Grade 8 POTW:
ReplyDeleteThe mean is 114.975.
There is no mode due to the fact that there aren't any repeating numbers in the set
The median is 110.45
The measure of central tendency that would most accurately be the mean, as it represents the average of all the numbers, so its more equally divided. I think that the 129.7 would be the outlier, as the other gas prices are much lower. Its really quite odd to see the first three Sundays to be quite low in price, but then the fourth would just be so costly. For example, this situation could occur in the real world. During the first few weeks, they were using a cheaper gas as a temporary substitute.
Grade 7 POTW
ReplyDeleteLined up in order, the numbers are
$35,000, $36,000, $38,000, $39,000, $40,000, $42,000, $42,000, $74,000
Mean: All the numbers added together sums up to $346,000
Divide it by 8, the amount of numbers present in the survey, and we are left with $43,250 as the mean.
Median: The two numbers in the middle of the lineup would be $39,000 and $40,000. In order to find the median here, I need to add the two numbers then divide them by two. In this case, the median is $39,500.
Mode: This data set contains two $42,000's, while all the other numbers only show up once. Therefore, $42,000 is the mode.
Range: The greatest number in this data set is $74,000, while the least is $35,000. The difference between those numbers are $39,000, making it the range.
Jessica's Salary: I believe that Jessica's salary would be $40,000. According to a survey from 8,118 employees, (https://www.indeed.com/salaries/Pool-Manager-Salaries?period=yearly) the pool managers had a yearly salary at around $39,312 per year. And the closest amount to that would be $40,000. So I believe that would be Jessica's salary.
GRADE 7 POTW
ReplyDeleteFinding the mean: In order to find the mean, all numbers have to be added up and the sum is divided by the amount of numbers in the data set. $35,000 + $42,000 + $36,000 + $74,000 + $38,000 + $40,000, $39,000 + $42,000 = 246,000. There are 8 numbers in the data set. 246,000/8 = 30750. Therefore the mean is 30,750.
Finding the median: In order to find the median, the data set must be ordered from the smallest to largest numbers. It will be in this order: $35,000, $36,000, $38,000, $39,000, $40,000, $42,000, $42,000, $74,000. The median is the middle number of the data set and if there are two, then its the mean of the two. The The median is $39,000 and 40,000. The mean of the two is $39,500. Therefore the median is $39,500.
Mode: The mode is the most frequently occurring number in a data set. For this data set, $42,000 is the only number that appears twice. Therefore the mode is $42,000.
Range: Finding the range is by subtracting the smallest number in the data set ($35,000), from the largest number ($74,000) The difference of $74,000 and $35,000 is 39,000. Therefore the range is $39,000.
Jessica's Salary: Considering the fact that Jessica is the pool manager, no matter how long employees have worked, the manager gets more pay. Jessica's salary should be $74,000. I think this because as stated before, a manager can still gain more salary than an employee that has served there for longer. I don't think the fact that David has served for so long that he gets the largest salary. There rare averages for different occupations. If Jessica were an employee, then David would most likely have the better salary of the two. Therefore Jessica's salary is $74,000.
I hope this test works
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteGrade 8 POTW:
ReplyDeleteMean: To get the mean You have to add all the numbers and divide the sum by the amount of numbers you add together.
109.8 + 109.3 + 111.1 + 129.7 = 459.9
459.9 / 4 = 114.975.
The mean is 114.975.
Median: The median is the middle number. If there are two middle numbers then the median is the average of those two.
109.8, 109.3, 111.1, 129.7
The middle two numbers are 109.3 and 111.1. The average of those two is:
109.3 + 111.1 = 220.4
220.4 /2 = 110.2
The median is 110.2.
Mode: The mode is the number that repeats the most. None of these numbers repeat so there is no mode.
There is no mode.
I think that the most accurate central tendency to represent this data set. The reason for this is because there is an outlier, 129.7. It about 20 above all of the other number which are around 1 apart. This makes the messes up the mean, making it very high when most of the numbers are much less than it. The mode shouldn't be used because there is none which leaves median.
I think that the most accurate central tendency to represent this data set.
I believe that the reason there is an outlier because the oil availability took a hit from something like a natural disaster. I know that hurricane Harvey recently came and the oil prices increased a lot because of it.
I messed up the median.
Delete109.3, 109.8, 111.1, 129.7
The middle two numbers are 109.8 and 111.1. The average of those two is:
109.8 + 111.1 = 220.9
220.9 /2 = 110.45
Test
ReplyDeleteGrade 8 POTW
ReplyDeleteMean: 114.97
To get the mean, you must add up all the numbers together, and divide by how many numbers there are in total.
109.8 + 109.3 + 111.1 + 129.7= 459.9
459.9/4= 114.975
Mode: Nothing
The mode is the number that is repeated throughout a set of numbers. Since all of the numbers in this set were different, there is no mode
Median: 110.2
The median is the middle number in a sequence of numbers. Since this set of numbers had an even number of them, meaning there were two middle numbers, we must find the mean of those two numbers.
109.3 + 111.1= 220.4
220.4/2= 110.2
Outliers: After August 30th, the gas prices started to jump quite high, meaning the outlier would be 129.7. This is because 129.7 is much higher than the other numbers in that number set.
There also seems to be an upward trend, since like I said before, the prices jumped around August 30th onward.
I feel that the most accurate central tendency is the mean. This is because you are finding the overall (more or less) average of the set of numbers. Therefore you're not just using the middle number, or other methods. It is the average of the set.
Now around the time that gas prices spiked was during Hurricane Harvey, or when it was starting to recede. There was a lot of damage, which does play a role with this, but also the amount of flooding. There was a widespread of flooding especially in Texas. The refineries along the Texas Gulf Coast actually had to shut down, to protect them from more potential flooding. That means more than 15 percent of America's oil refineries are shut down!
As well, OPEC has made an agreement to cut down on oil production, along with implanting carbon taxes to help reduce the carbon emissions to help with climate change, etc. That has also had a big impact on the gasoline prices.
Grade 8 POTW
ReplyDeleteMean:
To get the mean, the numbers must be added up and divided by the amount of numbers there are in total
(109.3+109.8+111.1+129.7) / 4
=459.9 / 4
=
Median:
To find the median, the numbers are lined from smallest to largest to find the middle number. Because there are an even amount of numbers, add both of them up and divide the number by 2
(109.8+111.1)/2
=110.45
The median is 110.45
Mode: No mode. This is because mode is the number that is most repeated. In this case, there are no repeating numbers.
The outlier in this data set is 129.7. This is because it is much higher than the other numbers. It is around 20 cents more than others, while the 109.3,109.8, and 111.1 are just apart by a few decimals.
It seems to have an upward trend starting form 8/23 because from that date, it only rose and did not decrease.
The most accurate central tendency is the median. This is because when there is an outlier, the average increases. Also, there isn't a mode in this data which means the median is the most accurate.
The rise in gas price is because of 10 major refineries being closed. The reason of the closure is because of Hurricane Harvey. Since the refineries were closed, 15% of America's fuel production is cut. Almost 3 billion barrels were cut of the 18 billion daily barrels.
I forgot the mean
DeleteMean:114.975
Testing
ReplyDeleteGrade 7 POTW
ReplyDeleteMean/Average: Adding all of the numbers together and dividing the sum by the total amount of numbers.
35,000 + 42,000 + 36,000 + 74,000 + 38,000 + 40,000 + 39,000 + 42,000 = 346,000
346,000/8 = 43,250 (Since there are 8 numbers in total, I divided the sum but 8)
The mean of the salaries is $43,250
Median: Ordering the numbers from lowest to highest and pinpointing the number in the middle.
Numbers from lowest to highest:
$35,000, $36,000, $38,000, $39,000, $42,000, $42,000, $40,000, $74,000
There are two numbers in the middle: 39,000 and 42,000. So I found the average of the two numbers.
39,000 + 42,000 = 79,000
79,000/2 = 39,500
Since there are only two numbers now, I divided 79,000 by 2.
The median is $39,500.
Mode: The number that occurs the most.
$35,000, $36,000, $38,000, $39,000, $42,000, $42,000, $40,000, $74,000
All of the number only occur once, except for 42,000 which occurs twice. Therefore, $42,000 is the mode of the salaries.
Range: The difference between the largest and the lowest numbers.
$35,000, $36,000, $38,000, $39,000, $42,000, $42,000, $40,000, $74,000
When I put the numbers in order from lowest to largest, the lowest number was 35,000 and the largest number was 74,000. Then to find the difference between the two numbers I subtracted 35,000 from 74,000.
74,000 - 35,000 = 39,000
The difference is 39,000 which means the range of all of the salaries is $39,000.
I think that Jessica's salary is the most, $74,000. Since all of these salaries are from people who work at the pool, I think the manager would have the highest salary. Jessica is technically David's "boss" since she is the manager and he is just an employee. Even though David has been working longer than her, Jessica is of higher position, so I believe that she would get paid the most.
Mean:
ReplyDeleteTo find the mean, I must add all the numbers together, then divide it by the number of numbers there are
35,000 + 42,000 + 36,000 + 74,000 + 38,000 + 40,000 + 39,000 + 42,000 = 346,000
$346,000/ 8 = $43,250
The mean of the data set is $43,250
Median:
To find the median, I have to order the set from least to greatest, the find the middle number
$35,000, $36,000, $38,000, $39,000, $40,000, $42,000, $42,000, $74,000
$39,000 + $40,000 = $79,000
$79,000/2 = $39,500
Mode:
I have to find which number appears the most
$35,000, $42,000, $36,000, $74,000, $38,000, $40,000, $39,000, $42,000
$42,000
Range:
I have to subtract the smallest salary from the largest one.
$74,000 - $35,000 = $39,000
I think Jessica's salary is $74,000. Since she is the manager, she probably gets the highest salary. Even though David has been working at the pool the longest, that doesn't mean that he gets paid the most. Jessica's position is also a higher position.
Grade 8 POTW
ReplyDeleteI think that the mean gas price on Sunday is 114.97
I think this because in order to get the mean you have to add all the numbers and then divide the sum by the number of numbers there are in total.
109.8 + 109.3 + 111.1 + 129.7= 459.9
459.9 divided by 4 = 114.975
There is no mode. That's easy.
The median is 110.2
The median is the middle number once you align the numbers
Ivan shepelev
ReplyDeletegrade 7 POTW
mean=43,250
mode=42,000
median=39,500
i found the mean by first adding all the numbers together then dividing them by the amount of numbers witch is 8
35,000 + 42,000 + 36,000 + 74,000 + 38,000 + 40,000 + 39,000 + 42,000 = 346,000
$346,000/8 = 43,250
mean= 43,250
i found the mode buy finding the number that has the most doubles
35,000 (42,000) 36,000 74,000 38,000 40,000 39,000 (42,000)
mode= 42,000
i found the median buy buy ordering the numbers from highest to lowest then adding 39,000 and 40,000 then dividing buy 2
35,000 42,000 36,000 74,000 38,000 40,000 39,000 42,000= 35,000 36,000 39,000 40,000 42,000 74,000
39,000+40,000=79,000
79,000/2=39,500
median= 39,500
i think Jessica's salary is 74,000 because she is the manager
Grade 8 POTW:
ReplyDeleteThe mean for the gas price is 114.975 (109.8+109.3+111.1+129.7=459.9÷2= 114.975)
There is no mode, no numbers are repeated.
The median is 110.45, in order for me to get the answer I simply added the two middle numbers, which happened to be 109.8 & 111.1. Once I figured that out I dived it by two.
There is a outlier, which is 129.7 I believe. This is because it is higher than the other numbers by about 20, it goes from 111.1 to 129.7.
First Grade POTW
ReplyDeletei found the mean buy adding all the numbers together and then dividing them buy the amount of numbers
35,000 + 42,000 + 36,000 + 74,000 + 38,000 + 40,000 + 39,000 + 42,000 = 346,000
$346,000/ 8 = $43,250
mean= $43,250
i found the median buy finding the numbers closest to the middle when in lest to greatest then i add the 2 and divide buy 2
$35,000, $36,000, $38,000, $39,000, $40,000, $42,000, $74,000
$39,000 + $40,000 = $79,000
$79,000/2 = $39,500
median=$39,500
i found the mode buy finding the most common number witch is 42,000
The mean would be 114.975, this is because 109.8 + 109.3 + 111.1 + 129.7 = 459.9. Once I got that answer I simply divided 459.9 by four.
ReplyDeleteThere is no mode, as there is no repeated numbers
The median is 110.45. I got this answer by aligning the numbers from least to greatest and added the two numbers in the middle, which were 109.8 and 111.1, once that was done I added those two numbers together and divided it by two, which got me the answer of 110.45
The outlier in this data set would be 129.7, this is because it spikes up form the number before which is 111.1.
Grade 8 POTW:
ReplyDeleteMode: There is no mode since no numbers in the data set repeat more than once
Median: The 2 middle numbers are 109.8 and 111.1. To find the median, we have to add those two up and divide by 2 afterwards. When adding the 2 up, I got 220.9. Then when I divide that by 2, I got 110.45.
Mean: To find the mean, I have to add all 4 numbers and divide the sum by 4. I got 459.9 after adding all 4 numbers up. After diving that by 4, I ended up with a mean of 114.975.
I think that the best CT to find the average of the data set would be the median. I reason why I chose this was because I noticed that there was an outlier in the data set (129.7) which would mess up the average if we used the mean. The median on the other hand forgets all about that outlier and instead uses the 2 middle numbers to find the average.
There IS an outlier in the data set. I think this outlier would be there because of the recent outbreak of Hurricane Harvey. This would increase the gas prices a whole lot as places all around the world would have to compensate to everything lost and closed in the massive floods.
There is an upwards trend in the graph nearing the end of the month which is when Hurricane Harvey had just started to become disastrous. The gas prices would've had to have been upped due to availability of oil.
GR7 POTW
ReplyDeleteRyan
Mean 43,250 because the mean is basically the average which is calculated by adding up all the numbers and dividing the sum by the total amount of numbers listed to get 43,250
mode:42,000 this is because the mode is the number that appears the most -> (list) 42000 42000 35000 36000 38000 39000 40000 74000. Which happens to be 42000 which appears twice over once from the other numbers.
Median: 39500. This is the median because the median is the middle number. Since there is an even amount of numbers in the list the ,median would have to be in between two of the numbers ( 40,000 and 39,000) to equal 39,500.
I think that Jessica's salary would be 74,000. I think this because if she is the pool manager, she would probably earn more then volunteers and just average pool employees since she is at a higher level then all the others so I think she would be paid more then others
Mean: (109.8 + 109.3 + 111.1 + 129.7) divided by 4 = 114.9
ReplyDeleteMedian: 110.45
Mode: no mode
The mean is 114.975, the median is 110.45 and there is no mode. The reason for the outlier on the last Sunday because of Labour day and hurricane Harvey closing oil refineries.
ReplyDeleteGrade 7 POTW
ReplyDeleteMean: 43,250 Median: 39,500 Mode: 42,000 Range: 39,000 Jessica’s salary: $74,000
First I added $35,000, $42,000, $36,000, $74,000, $38,000, $40,000, $39,000, $42,000 and got 346,000. I then divided 346,000 by 8 which is the amount of numbers given to get 43,250 as the mean. Next, I put all 8 numbers in order from lowest to highest like this $35,000, $36,000, $38,000, $39,000, $40,000, $42,000 $42,000, $74,000. I started to cross out the highest and lowest number simultaneously leaving 39,000 and 40,000. Since there were two middle numbers, I added 39,000 and 40,000 to get 79,000. All I needed to do to get the median, is divide 79,000 by two to get the quotient of 39,500. Finally, to get the mode, I looked for the numbers that are most common. I noticed that 42,000 is the most common number giving me the mode. To find the range, I lined up all the numbers from least to greatest. I then subtracted 35,000 which is the lowest number by 74,000 which is the highest to get the range of 39,000. I think Jessica’s salary is $74,000. I know the boss will probably get paid more than the manager, but it never said that the boss got surveyed. It said that only Jessica and all the pool employees. Usually, the managers get paid more than the employees no matter how long an employee has worked there.
First I decided to work with the mean. I added up all 4 of the quantities and came out with 459.9. From here since I added up 4 values, I need to divide by 4.
ReplyDelete459.9 / 4 = 114.975
Now I can do the median. I first have to order the numbers.
109.3, 109.8, 111.1, 129.7
Since however there is no middle number I must find the middle of the 2 middle numbers. After doing this I came out with 110.5.
Now because there are no equal numbers there is no mode.
No Mode
Median is 110.45
Mean is 114.975
A reason that may contribute to the last Sunday which is an outlier, could be the fact that many oil companies and refineries might have been closed due to certain weather problems, meaning there was little oil being produced.
The mode of the salary is 42,000, the mean is 43,250, and the median is 40,500. The range of the salaries is 35,000 - 74,000. I think that Jessica would have a salary of 42,000 because she doesn't have the most important job, but still has a relatively important job.
ReplyDeleteFirst, believe the mean of the maple pool is 43,000 because all the salaries combined and divided by 8 (number of salaries) equals 43,00 according to the math I did. The median is 39,500 because between 39,000 and 40,000 that's the half mark. The mode is 42,000 because it appears twice. I think that Jessica's salary would be 40,000 because Jessica controls a section of people depending their lives on her. If Jessica commands all life guards should not come tommorow or makes a very horrible decision, people in the pool, may drown or get disappointed in her and the community centre. Sure people's lives depend on her, but she is expected to not let anyone drown and control many things related to the pool. There are people who have more important jobs like the whole runner of the community centre who deserve more than she does. Like David, many of the staff probably know him cause he has been their for quite a while, so if you know more about them, you probably also no their strengths so, David may probably get 42,000.
ReplyDeleteThis is how I went about solving the Grade 8 POTW:
ReplyDeleteMean:
109.8 495.5 / 4
+109.3 = 123.875 ≈ 123.88
+111.1
+129.7 Therefore, the mean is 123.88 cents.
Median:
109.3, 109.8, 111.1, 129.7
111.1 1.3 / 2 = 0.65
-109.8
------- 109.8 + 0.65 = 110.45
1.3
Therefore, the median is 110.45.
Mode:
N/A
Median would be the most effective to represent this data set because 129.7 is an outlier and throws off the mean data.
The outlier would be 129.7 because it is nearly 20 more than the others.
Hurricane could be the reason the gas prices were raised because it cut out the power and availability of oil would be low.
- Ameya
Ameya, I think you should re-check your addition for the mean
DeleteThis is how I went about solving the Grade 8 POTW:
ReplyDeleteMean:
109.8 495.5 / 4
+109.3 = 123.875 ≈ 123.88
+111.1
+129.7 Therefore, the mean is 123.88 cents.
Median:
109.3, 109.8, 111.1, 129.7
111.1 1.3 / 2 = 0.65
-109.8
------- 109.8 + 0.65 = 110.45
1.3
Therefore, the median is 110.45.
Mode:
N/A
Median would be the most effective to represent this data set because 129.7 is an outlier and throws off the mean data.
The outlier would be 129.7 because it is nearly 20 more than the others.
Hurricane could be the reason the gas prices were raised because it cut out the power and availability of oil would be low.
Grade 8 POTW:
ReplyDeleteThe mean gas price of the last 4 Sundays is 114.975 cents per litre.
The median gas price of the last 4 Sundays is 110.45 cents per litre.
There is no mode.
I believe that the mean is the most accurate way to represent the data. This is because it isn't too close to the lowest value of 109.3 and it is the closest to the highest value of 129.7. It is also very close to the middle values and it shows a good representation of the prices.
There is an outlier of 129.7 because it is about 18 cents more than the next highest value which is 111.1 cents per litre because tere is a low of gas and those gas stations want money.
Am RWA for outliers for this is gas because sometimes gas goes very cheap when they find a lot and the prices can go very high when there is a "shortage." Gas prices also tend to be cheaper around midnight compared to the daytime because less people fill up their gas at that time.
data set: 109.3, 109.8, 111.1, 129.7
ReplyDeleteaverage: to find the average, add all the numbers in the data set and divide them by how many numbers you added. in this case, the numbers add up to 459.9 .
and because there are four numbers it is required to divide by 4 equalling: 114.975
the average is 114.975
median: to achieve the median number order all the number form greatest to least (or the other way):
109.3, 109.8, 111.1, 129.7
then find the number in the middle of the data set.
if the data set contains an even number of data pieces than take the two center data pieces and add them together: 220.9
then divide them: 110.45
the median is: 110.45
the mode of the data set is the number that repeats itself the most.
but in this case there is no mode.
There are lots of great answers and solutions above. I am wondering why there are a few different answers for the Grade 8 mean answer though. Can anyone see why? I keep getting 114.975, but I've seen other answers, such as 123.88.
ReplyDeleteMost people got 114.975 including myself. I looked at the process for the person who got 123.88. I think he just added a little wrong because when he stated the sum, it was off a bit. I think that's why.
DeleteFirst I will find how much all his kicks should add up to by multiplying the mean/ average by the number of kicks there were:
ReplyDelete35 yards x 5 = 175 yards
I know that his furthest kick is 44 yards, so I should subtract it from the total.
175 yrds - 44 yrds = 131 yrds
Now the rest of the kicks should add up to 131 yards, but none of them can be greater than 44 yards. I know that the smallest positive integer is 1, so I can try using that.
131 - 1 = 130
Now the last 3 kicks should add up to 130. The last three kicks could be any numbers, just bigger than 1 and smaller than 44. The three kicks can be: 43, 43, and 44. Since 44 isn’t larger than his longest kick, it could be a possibility.
His kicks are 1, 43, 43, 44 and 44.
Double check: 1 + 43 + 43 + 44 + 44 = 175
175 / 5 = 35
The mean is 35
The median is 43
The mode is 43 and 44
The range is 43
just saying as a fyi, it states each kick was a different positive integer
DeleteBut the question above is POTW #1?
Deleteso basically what i did was i did the equation backwards aka reverse engineering.
ReplyDeletefirst i have to find what all of the integers add up to
so i did 35 x 5 which is the mean multiplied by how many kicks which got me 175.
then i can just add up the numbers which are lower than 44. so it was 44, 43, 42, 41, added all together got me 170. i had to do it this way because the question states that all integers must be different and lower than 44. so to find the lowest possible hit, i would have to make all the other hits the biggest possible.
once i got 170, i subtracted that from 175, being all of the integers added up, and got 5.
so in conclusion, the lowest possible hit that khan kickit could have got was 5.
But the question above is POTW #1? And PLEASE DAVID, use COPS! (punctuation, spelling, etc.)
DeleteThis comment has been removed by the author.
ReplyDeleteCole's POTW #2
ReplyDelete44, 43, 42, 41, 5
The minimum possible length of Khan’s shortest kick is 5 yards. I know this because if Khan’s longest kick is 44 then that means all of the number after have to be less than that. Since in the question it said that each of his kick is a different integer the only way to get the shortest amount of yards is if I add the highest four numbers I can. The four numbers are 44, 43, 42, and 41. I know this because each number has to be different and they all have to be less than 44. After multiplying 35 by 5 I got 175 which must be the sum of all 5 kicks. I also found out that 44+43+42+41= 170 so the lowest possible number possible would have to be 5 yards. The minimum possible length of Khan’s shortest kick is 5 yards
First, I needed to figure out how many yards there were in total. Since the average was 35 and there were 5 kicks in total, I did:
ReplyDelete35 x 5 = 175.
Since I know that the largest number of yards was 44, I did:
175 - 44 = 131
Since 130 is easier to work with, I guessed that the smallest number of yards was 1 and did 131 - 1 which gave me 130. From there I had to check if 3 more kicks could get me to 130.
I guessed 43, 42, and 41. But when I added all of the kicks, I only got 171.
Since I know that 1 was too small to be the smallest number and I was short by 4, I did 1 + 4 = 5. So then I knew that the smallest number was 5.
I need to find out how much his kicks add up to, which will be my first step. The mean, (35) multiplied by how many kicks he made resulted in 175. (35 x 5)
ReplyDeleteI know that one of his kicks was 44 yards, and that it was the kick that went the farthest, so everything else must be less than 44 yards. Each of his kicks was a different positive integer length, which is also important information, and all integers (the kicks) were different.
As a result, however, of the fact there was nothing I could actually work with without having to guess completely, I figured that it would make sense to start with three numbers lower than 44, and then for the last number, add all the previously chosen numbers together and then subtract the total from 175 to find our last number.
So I'm going to choose the numbers that are smaller than 44, which I will guess. I have to keep in mind, however, that the last number CANNOT be larger than 44, as 44 is already the furthest kick. So I will start with 43. I need to keep in mind the result has to be smaller, so the next number will be 42. I will continue with 41.
I also need to keep in mind that there is already 44, which is his farthest kick. So I will subtract 44 from 175, which results in 131. Then I will add 43 and 42 together, which is 85. 85 subtracted from 131 is 46. Already, we can easily make the next two numbers.
I do need to make the number SMALLER than 44, though. That'll be easy, though. We'll just take the next possible number, which is 41. Now to find the next number, I need to subtract 41 from the remaining number, 46. And the last number is 5.
So, as a result, Khan Kickit's ("Kick It"?) shortest kick was three yards.
(I commented this before but made a mistake, as I used 43 twice. For this comment, I thankfully fixed it. Yay!)
Bhavee's Grade 7 POTW #2
ReplyDeleteSince the average is 35, and he kicked five times, we would get a rough answer of all the scores added up, but we know that one of the five kicks was 44 for sure, so we minus 44 from 175, which is 131,35X5. Now we temporarily cross of 44 because we already covered that and move on to another kick. Since all kicks were different, and 44 was the highest, the three lowest after 44 are 43, 42, and 41, maybe not in that order, but probably those numbers else the average wouldn't be what it is. So Kick 1: 44 Kick 2:43 Kick 3:42 Kick 4 (The lowest, we don't know. Since we don't count 44, we add up 43, 42, and 41, which adds up to a sum of 126. We would now minus 126 from 131, which gives us a answer of 5.
test
ReplyDelete
ReplyDeleteThe shortest kick is 5 yards. Since the average is 35, I simply multiplied the average by 5 for every punt Khan did to get the sum I should get when finding all the longest lengths that Khan kicked using a football. The sum is 175. Knowing that the longest punt was 44 yards, I went done by 1 yard each time in order to find the 4 longest possible kicks Khan can do. I got 41, 42, 43, and 44. The sum of the four adds up to 170. Therefore leaving 5 left to be the shortest kick Khan did. The shortest kick Khan could do is 5 yards.
Longest: 44 yards
Shortest: 5 yards
Mean: 35 yards
35 * 5 (For each punt) = 175
5 + 41 + 42 + 43 + 44 = 175
175/5 = 35 yards
POTW #2:
ReplyDeleteFirst of all, to find an average, you have to find the sum of all the numbers, once you have that answer divide it by the sum.
X=Sum of tokens
N=Amount of tokens
56x=55x+68 I think. So if you simplify it will be 1x=68. That would mean that there are 68 tokens in the bag??
So therefore the amount of tokens in the bag, which is 68 multiplied by the average value of the tokens. which happens to be 56 is 3808
With the remaining 67 tokens it can be assumed to be 1 in order to get the largest possible value. 3808-67=3741. So therefore the largest possible integer for the average to be 56 is 3741
The lowest possible punt range is 5 yards. I originally did 44 44 44 42 and 1, but then when I checked with Esther she said all the integers had to be different. From there I troubleshooted to get to 44 43 42 41 and 5. To do that I moved each of the 44's down except for one, by one, and kept the one. Than I tried doing that and came with 34.2. Than I did 8*5 and got 4. I added 4 to 1 to get five and checked. Than I found that 44+ 43+ 42+ 41+ 5= 175 and 175/ 5=35. That is how I got my data set.
ReplyDelete