POTW #3 Solution:
Grade 7 POTW #4 Question:
Aliyah had a great 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, Aniya,
volunteers to go first, while its longest serving employee, Simon, decides to go
second. Aliyah surveyed the salaries of all the pool staff and finds the
following annual salaries:
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, Aniya,
volunteers to go first, while its longest serving employee, Simon, decides to go
second. Aliyah 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? What is the median? The mode? What is the range of the salaries?
Which salary is probably Aniya’s salary? Why do you think that?
Which salary is probably Aniya’s salary? Why do you think that?
Grade 8 POTW #4 Question:
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):
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 do some
research).
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 do some
research).
POTW 4
ReplyDelete(Leah)
First I need to order the numbers least to greatest. 35,000, 36,000, 38,000, 39,000, 40,000, 42,000, 42,000, 74,000. Added up, they equal 346,000. Divided by 8 (there are 8 salaries) it is 43,250. That means the mean is $43,250. The median is $39,500. I know this because I crossed numbers off from the two ends and found the average of the two middle numbers. The mode is the most common number which in this case, is $42,000. The range is 74,000 minus 35,000 which is 39,000 so the range is $39,000.
Mean- $43,250
Median- $39,500
Mode- $42,000
Range- $39,000
I think Aniya’s salary would be the $74,000 because in the real world, managers often get paid a lot more, even more than someone who has been there for a while (simon).
Mean:
ReplyDeleteTo find the mean, I have to add all the salaries up, then divide the sum by the number of salaries (8).
$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 salary is $43,250.
Median:
To find the median, first I have to order the salaries from least to greatest. After that, I will cross out the salaries from each end until I remain with only 2 salaries (since the data set has an even amount of salaries. After that, I will find the average of those two remaining salaries to reach the median.
$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
The median salary is $39,500.
Mode:
To find the mode, I will basically look for the most occuring salary in the dataset.
$35,000, $42,000, $36,000, $74,000, $38,000, $40,000, $39,000, $42,000
The mode salary is $42,000.
Range:
To find the range, I will subtract the smallest salary from the greatest salary, the difference will therefore be the range.
Biggest salary=$74,000
Smallest salary=$35,000
$74,000-$35,000=$39,000
The range is $39,000.
I think that the greatest salary, $74,000, is Aniya’s salary. Even though Simon is the longest serving employee, managers get a higher salary. If Simon’s skills were worth a lot, he would probably get paid more than Aniya. But since that usually only happens in stores involving electronics, I think Aniya’s pay would be the highest.
Mean: 346000 / 8 = 43250
ReplyDeleteMedian: 39.5
Mode: 42k
Range: 39
I think Aniya’s salary is 42,000 because when I searched up average salary of a pool manager 42,000 popped up
Extension: 42,000 divided by how many hours in a year(24 x 365 = 8,750)
To find the mean, you can add all the numbers and divide the sum by the total number of numbers. When you add them all, it is 346000 and when you divide it by 8 it is 43250 dollars. To find mode, find the number that occurs the most in the data set, which is 42000 which occurs twice while all the others only occur once. To find median order the numbers from least to greatest and the median is the number in the middle. 35000 36000 38000 39000 40000 42000 42000 74000. Since there are eight numbers we will use numbers 39000 and 40000, so we add them and divide by 2 which is 39500. The range is the lowest number subtracted from the highest number. 74000-35000=39000.
ReplyDeleteThe mean is $43250, the mode is $42000, the median is $39500 and the range is $39000.
Since Aniya is the manager, she would probably be paid more because she supervises, and in real life the manager gets more money, even if someone has been there longer like Simon.
Before I figure anything out I need to put all the numbers in order:
ReplyDelete$35,000, $36,000, $38,000, $39,000, $40,000, $42,000, $42,000, $74,000
Now the Mean:
Total of all Salaries: $346,000 $346,000/8 = $43,250(Mean)
Next the Median: (because I can't strikethrough I will put an ❌beside all I want to strikethrough)
$35,000❌, $36,000❌, $38,000❌, $39,000, $40,000, $42,000❌, $42,000❌, $74,000❌
I will now find the average of the two middle numbers: $39,000+$40,000= $79,000/2 = $39,500(Median)
Now the Mode:
Now looking at the data set the only number that repeats itself is $42,000(Mode)
$35,000, $36,000, $38,000, $39,000, $40,000, $42,000, $42,000, $74,000
Lastly the Range:
$74,000 - $35,000 = $39,000(Range)
Now I am going to estimate which salary might be Aniya's: I am going to one by one delete numbers and give explanations.
$36,000, $38,000, $39,000, $40,000, $42,000, $42,000, $74,000 (full data set for reference)
I will first delete the 4 lowest salerys becuase since Aniya is a manager she would get paid more.
$42,000, $42,000, $74,000 (Salery's left)
I will now say that Aliyah and Simon will both get paid $42,000 because Simon has been there longest and Aliyah's job is important.
$74,000
Now that this is the only salery left it is Aniya's. I think this because a manager is a very important job and should pay quite a bit of money.
New phone, who 'dis?
DeleteGrade 8 POTW:
ReplyDeleteFind:
- Mean Sunday price
- Median Sunday price
- Mode Sunday price
The following prices are for Sunday:
- 109.8, 109.3, 111.1, 129.7
Mean: 114.975 cents per litre
Median: 110.2 cents per litre
Mode: No Mode
The median best represents the majority of the data because the first 3 prices are less than 1 away from the median. The only outlier would be 129.7. This could be because supply and demand were in an imbalance. There could be more demand than supply, so they had to raise the price to correct the imbalance. There is a trend until the sudden spike at the end of August. This could be because more parents and students start to travel more during September because of school and work. This is a good marketing strategy because more people are "forced" to buy more gas because they need to travel more.
Grade 7 POTW
ReplyDeleteThe central tendency of all of the salaries are listed below.
Salaries: 35,000 42,000 36,000 74,000 38,000 40,000 39,000 42,000
Mean:346,000 divided by 8= 43,250
Median: 2 middle numbers= 39,000 and 40,000. 39,000 plus 40,000= 79,000 divided by 2 39,500
Mode: 42,000 appeared 2 times which was the most.
Range= Largest number= 74,000 and smallest number= 36,000 74,000 - 36,000= 38,000
I think that Aniya's salery is either 74,000 or one of the 42,000 saleries becuse pool manager is one of the most important jobs in the center probably. If Aniya should get one salary, I think it should be 74,000 becuase the manager is technically the boss of something and the manager of the pool is the boss of the pool so yeeeeeaaaaaa. Simon and Aliyah should rightfully get the 42,000 salaries as they are the next 2 important employees/workers at the community center.
I had already done this POTW in Mr Milne's class should I do this again?
ReplyDeleteThat's not necessary. Thanks for asking though Carlo
DeleteGrade 7 POTW
ReplyDeletemean - $35,000 + $36,000 + $38,000 + $39,000 + $40,000 + $42,000 + $42,000 + $74,000 ÷ 8 = $43,250
median -$3̶5̶,0̶0̶0̶, ̶$3̶6̶,0̶0̶0̶, ̶$3̶8̶,0̶0̶0̶, $39,000, $40,000, $4̶2̶,0̶0̶0̶, ̶$4̶2̶,0̶0̶0̶, ̶$7̶4̶,0̶0̶0̶
39,000 + 40,000 ÷ 2 = 39,500
mode - 42,000
range - 74,000 - 35,000 = 39,000
I think that Aniya's salary should be either 42,000 or 74,000 because the pool managers job is still very important. Simon might get the highest one because he is the longest working employee so hes probably been promoted and has a high rank/job payment.
Maksim
ReplyDeleteThe mean is $43250 because if you add up all of the salaries, and then divide by 8 (number of salaries) then that is what you get
The median is $39500 because the 2 middle numbers are 39000 and 40000 and (39000+40000) divided by 2 is 39500
The mode(number that occurs the most) is $42000
The range is $39000 because the largest number-74000 - the smallest number- 35000 is 39000
I think that in real life Aniya should get either $74000 or $42000 because first of all managers get a lot of money. Also, the pool is one of the most used places in the community center so that is why she would get a high salary
Anya
ReplyDeleteMean- 35000+36000+38000+39000+40000+42000+42000+74000= 346000
346000/8= $43520
Mode- 42000
Median- 35000, 36000, 38000, 39000, 40000, 42000, 42000, 74000
79000/2= 39500
Range- 74000-35000= 39000
I feel Aniya's salary should be 74,000 although it said Simon works the most he could just be a high school student working as a swim instructor and other volunteer inactivates, in my experience I know that the manager runs the place and is the boss of everyone so speaking like that Aniya should get 74000
POTW #4:
ReplyDeleteMEDIAN: $39, 500:
To find the median, we order the numbers from least to greatest - $35,000, $36,000, $38,000, $39,000, $40,000, $42,000, $42,000, $74,000.
Now we find the 'middle' number, in this case, there are two, $39,000, & $40,000. We add them together, and divide by 2.
(39000 + 40000) / 2 = 79000 / 2 = 39,500
The median is $39,500.
MODE: $42,000
The most frequent number is $42,000.
MEAN: $43,250
We need to add all numbers together, then divide by 8, the total amount of numbers.
($35,000 + $36,000 + $38,000 + $39,000 + $40,000 + $42,000 + $42,000 + $74,000) / 8 = 346,000 / 8 = $43250
The mean is $43,250.
RANGE: $39,000
To find the range, we need to subtract the salary with the least amount of value from the salary with the greatest value:
$74,000 - $35,000 = $39,000
The range is $39,000
I believe Aniya's salary would be either $74,000 or $42,000; the highest salaries because the manager has a lot of pressure and responsibility, organizing and directing different tasks. They have control and are at the top of the 'job pyramid' meaning she would get paid more money then say, the longest serving employee. This is because even though the employee has worked with this business for a long time, the type of task they specialize in determines their pay.
(Ethan)
ReplyDeleteMEAN: All salaries added up adds to $346,000. Then, dividing the value by 8 (the number of salaries (or the number of people) there were) the answer would be $43,250.
MEDIAN: Lining all the salaries up in order would cause two numbers to be in the middle: $39,000 and $40,000. If you have two numbers in the middle, the average of the two is the median. SO, 39,000 + 40,000 = 79,000. 79,000 / 2 = 39,500.
Mode: The most frequent salary (there are 2 people with the same salary, the rest have unique salaries) is $42,000.
Range: The greatest salary ($74,000) - the smallest salary ($35,000) = $39,000.
I think Aniya's salary, as she was responsible for managing all the other employees' salaries, would be relatively high because managing lots of other people is not easy. Therefore, I think her salary would be $72,000, the highest one.
To find the mean you would do:
ReplyDelete$35,000 + $36,000 + $38,000 + $39,000 + $40,000 + $42,000 + $42,000 + $74,000 = $346,000 / 8 = $43,250
This equation shows us that the mean is $43,250.
Next, the median is $39,500 because the two numbers in the middle are $39,000 and $40,000. If you find the mean of these two numbers it will be $39,500.
The only number that occurs more than once is $42,000, so that is the number that can be the mode.
The range is $39,000, because $74,000 - $35,000 gives us the mode of $39,000.
I believe that Aniya’s salary is above $40,000, because she is a manager, and the rest of the salaries are probably for people who don’t have as high of a position as Aniya. Now, there are two numbers remaining, $42,000 and $74,000. I believe that Aniya’s salary is $42,000 for many reasons. First off all, there are two salaries that are at $42,000. This may mean that another manager, i.e. the manager of the fitness area may get the same salary as her, while the person who runs the library might get $40,000. Also, since Simon is the longest working employee, he must have worked up to earn the highest salary, and probably is the one with a salary of $74,000.
Therefore, Aniya’s salary is $42,000.
Grade 8 POTW
ReplyDeleteThe data set shows the cost of 1 liter of gas throughout each day. In this case, we were to only look at the past 4 Sundays. The past 4 Sundays' gas price per liter is 109.8, 109.3, 111.1, and 129.7. The mean of this data would be the sum of these 4 values divided by 4.
109.8 + 109.3 + 111.1 + 129.7 = 459.9
459.9/4 = 114.975
The median would be the values listed from least to greatest and then the mean or average of the middle values.
109.3, 109.8, 111.1, 129.7
109.8 + 111.1 = 220.9
220.9/2 = 110.45
The mode is the values in the data set that are repeated the most. There can be multiple modes or no mode. In this case, 109.3, 109.8, 111.1, and 129.7 only appear once so there is no mode.
The measure of central tendency that best represents the ENTIRE data set would be the median. This is because the median can represent near the middle of the trend line while disregarding the outliers (also why mean shouldn't be used). The mode would be good as well in this case as long as there is no mode, but the median represents more of the middle average while the mode is more specific to different parts of the trend line. For the Sunday central tendencies, it is the same concept, but the only different part is that there is no mode meaning that the best central tendency to be used can right away be decided as the median. There is a trend in the data set (briefly spoken about before). It is neither a positive nor negative trend though. This follows throughout until the outliers start appearing (there are outliers) near the end (new trend line may be forming). Reasons for the trend being quite consistent at a low level may be because it is during August where not too much is happening (vacations tend to occur during July and sometimes beginning of August). People also sometimes take day-offs + school-offs (second one is more of a mandatory thing) because it is the summer meaning a lot of the traffic and use of gas isn't TOO much. The outliers at the end may occur because September started and school and work may start again. Buses need lots of gas every day for dropping students off and picking them up. Parents and other adults may also drive to work, school, etc. Knowing all this, the people who decide the prices of the gas may change the amount to gain a slight increase in profit which ends up adding up.
It's the same journal but Aliyah is Esther, Aniya is Jessica and Simon is David
ReplyDeleteMath Journal #1
Esther’s Sweet Summer Job
11th September, 2018 Allen Liu
Introduction
Question
This math journal question is about Esther, who has a sweet summer job at the Maple Community Centre. Her job was making sure employees were paid well according to their jobs. She started with the pool. Jessica volunteers to go first, while the longest serving employee, David, went second. She collected all the pool staff’s salary, and arranged them in order:
$35000, $36000, $38000, $39000, $40000, $42000, $42000, $74000
What is the mean, median, and mode? Which salary do you think is Jessica’s salary? Why do you think that?
Given Info
We are given that Esther collected the annual salary of all 8 staff working at MCC pool. We are also given their salaries.
Required to Find:
We are required to find the mean, median and mode of the data set, as well as Jessica’s possible salary.
Application
We know the definitions of mean, median and mode to be, as listed,
Mean: The average of the values. Calculated by adding all the terms, then dividing by the number of terms. (𝑥 + 𝑦 + 𝑧 + 𝑤… )/Tn *Tn↝
Median: The “Middle Value” of all of the numbers arranged in order from least to greatest. If there are 2 median numbers, take the mean of the two.
Mode: The most commonly occurring number in a data set.
For the second half of the problem, we need to consider what the most likely scenario is. Jessica either volunteered to go first because she:
Wanted to prove she was manager and she should earn more
OR
Wanted to make a point on MCC’s good salaries.
As such, we can boil down the list based on those assumptions to two possible values: $74000 (She’s the manager; nobody earns more than her) logic, or $42000 (An unfair salary for a pool manager, but not ludicrously low).
As for David, they probably would be loyal to their longest serving manager, but there is a slim possibility that they are taking advantage because they are confidant he will remain loyal. I would place him at around $39000.
Solution
Executing the calculation for the mean, we get: (s+t+u+v+w+x+y+z)/Tn= (35000+36000+38000+40000+42000+42000+74000)/8= 346000/8= 43250. Therefore, the mean is 43250.
There are two median values, $39000 and $40000. Taking the mean, (39000+40000)/2= 79000/2= 39500. Therefore, the median is 39500.
The only number that occurred twice in the data set was 42000, therefore the mode is 42000.
Another interesting way to solve for median presented itself to me while I was looking at Calculus. Making a graph with the dataset and zooming in on a certain area of the graph, you can clearly see the median is 39500.
*just picture the graphs*
Statement
“Therefore, Jessica had a salary of $74000 annually, and David had a salary of $39000 annually. The mean, median and mode were, in their respective order, 43250, 39500 and 42000.”
I had to split this into two parts again
ReplyDeleteMath
35000+42000=77000
77000+36000=113000
113000+74000=187000
187000+38000= 225000
225000 + 40000= 265000
265000 + 39000 = 304000
304000 + 42000 = 346000
346000 / 8 = 43250
39000 + 40000 = 79000
79000 / 2 = 39500
Reflection
I felt like this was an easy way to start off the math journals, as we had been studying the topic of mean, median and mode over the past few years, so this was a mini-review for those kinds of subjects. Also, the logical inquiring for Jessica's Salary required quite some thinking, as it was a double-sided coin. That is why I rank the difficulty at 3.0/10.0.
I learned that the world of business isn’t always a glorious thing when putting my mind into the person who gives out salaries. Since David was so loyal, they could have underpaid him knowing he would stay. Jessica could have been one of the first people hired, so her salary might have been lower than normal, but MCC might have had trouble recruiting and gave higher salaries, which is why Jessica and David were the first ones to volunteer.
You could use this information in the real world when you are an accountant and have to find the average annual spending and taxes for an american family. Your judgement might be handy if you are working with the question “Where should I allocate their resources so that they could spend less?”
All in all, it was a math journal. I don’t have much else to say.
ReplyDeletefollowing annual salaries:
$35,000, $36,000, $38,000, $39,000, $40,000 $42,000, $42,000, $74,000,
What is mean salary? The mean salary is $346,000 divided by 8 which is 43,250. What is the median? The median is $39,500 The mode? The mode is 42,000 What is the range of salarys? 74, 000 + 35, 000= 39,000. And anyias is more than 40,000 because she is the manager.
ReplyDeleteMean is $43,250
Median is $39,500
Mode is $42,000
Range- $39,000
I think that Aniya would get paid the most because managers usually get paid more than a lower status. Most of the time even if you've been there longer doesn't mean you will receive more.