Mean, Median, and Mode: Homework

Even it out for the mean, line it up for the median, and look for repeats for the mode.

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Part A — The Mean: Even It Out / 7

For 1 to 3, even out the stacks so they're all the same height (sketch the blocks beside the problem if it helps). For all of them: add the numbers, count how many there are, and divide the total by that count.

1.
Even out stacks of 3, 5 and 7 blocks. How tall is each stack?Answer
2.
Even out stacks of 1, 4, 4 and 7 blocks. How tall is each stack?Answer
3.
Even out stacks of 6, 2, 9 and 3 blocks. How tall is each stack?Answer
4.
Find the mean: 12, 18, 15, 11Answer
5.
Find the mean: 40, 55, 70, 35, 50Answer
6.
Find the mean: 2.4, 3.1, 1.8, 2.7Answer
7.
Find the mean: 105, 98, 112, 101, 94, 110. Round to the nearest hundredth.Answer

Part B — The Median: Find the Middle / 6

Put the numbers in order first, every time. If two numbers are left in the middle, the median is halfway between them.

1.
13, 7, 21, 9, 15Answer
2.
44, 38, 51, 47, 40, 39, 50Answer
3.
6, 11, 3, 8Answer
4.
25, 30, 20, 35, 40, 45Answer
5.
1.5, 0.9, 2.2, 1.1Answer
6.
60, 61, 60, 75Answer

Part C — The Mode: The One You See Most / 5

Write the mode. Some sets have no mode, and some have two.

1.
5, 3, 5, 8, 2, 5Answer
2.
14, 12, 17, 12, 14, 19Answer
3.
21, 34, 18, 27Answer
4.
Favorite colors in a class: red, blue, blue, green, red, blueAnswer
5.
In 2, 9, 9, 9, 9, 4 a student writes 4 for the mode, because 9 showed up four times. What is the real mode?Answer

Part D — All Three, and the Traps / 7

For 1 to 3, find the mean, the median and the mode. For 4 to 7, each problem has a trap in it, so read carefully.

1.
9, 4, 6, 4, 7MeanMedianMode
2.
16, 22, 18, 16, 25, 23MeanMedianMode
3.
3.5, 2.0, 4.0, 2.5, 3.0MeanMedianMode
4.
Find the mean of 0, 10, 0, 20, 5. Do the zeros count?Answer
5.
A student says the median of 11, 4, 8, 2, 6, 15 is 8, because 8 is in the middle of the list as written. What is the real median?Answer
6.
Five scores have a mean of 12. Four of them are 10, 14, 9 and 15. What is the fifth score?Answer
7.
Can the median be a number that isn't in the set? Give an example.Answer

Part E — Real Numbers, and Which One Fits / 8

The calendar and the teams are real. For the last two, give the numbers and name the measure you'd use.

1.
The number of days in each month of a year that is not a leap year:
Month Days
January 31
February 28
March 31
April 30
May 31
June 30
July 31
August 31
September 30
October 31
November 30
December 31
a. What is the mean number of days in a month? Round to the nearest hundredth.Answer
b. What is the median? (There are 12 months, so there are two middle values.)Answer
c. What is the mode, and which month pulls the mean below 31?ModeMonth
2.
How many players each team has on the field or court at once:
Sport Players per side
Baseball 9
Basketball 5
Soccer 11
American football 11
Ice hockey 6
Volleyball 6
a. Find the mean.Answer
b. Find the median.Answer
c. What is the mode?Answer
3.
Maya's last five bowling scores were 110, 115, 112, 118 and 40, the night she hurt her wrist. Find the mean and the median. Which one better describes how she usually bowls?MeanMedianWhich one
4.
A shoe store is deciding which size to order the most of. Should it look at the mean, the median or the mode of the sizes it sold?Answer

Month	Days
January	31
February	28
March	31
April	30
May	31
June	30
July	31
August	31
September	30
October	31
November	30
December	31

Sport	Players per side
Baseball	9
Basketball	5
Soccer	11
American football	11
Ice hockey	6
Volleyball	6

Part F — Critical Thinking / 3

Write a set of numbers that fits each rule. The last one is yours to make up.

1.
Write a set of five whole numbers where the mean, the median and the mode are all the same number.Answer
2.
Write a set of five whole numbers where the mean is bigger than the median. What kind of number makes that happen?Answer
3.
Collect six real numbers from your own week, such as minutes spent reading each day. Find the mean, median and mode, and say which one describes your week best.Answer

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Total / 36

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Notes

Answer key

Part A — the mean.

5. 3 + 5 + 7 = 15 blocks, and 15 ÷ 3 = 5.
4. 1 + 4 + 4 + 7 = 16 blocks, and 16 ÷ 4 = 4.
5. 6 + 2 + 9 + 3 = 20 blocks, and 20 ÷ 4 = 5.
14
50
2.5
103.33 (620 ÷ 6)

Part B — the median.

13. In order: 7, 9, 13, 15, 21.
44. In order: 38, 39, 40, 44, 47, 50, 51.
7. In order: 3, 6, 8, 11, and halfway between 6 and 8 is 7.
32.5. In order: 20, 25, 30, 35, 40, 45, and halfway between 30 and 35 is 32.5.
1.3. In order: 0.9, 1.1, 1.5, 2.2, and halfway between 1.1 and 1.5 is 1.3.
60.5. In order: 60, 60, 61, 75, and halfway between 60 and 61 is 60.5.

Part C — the mode.

5. It appears three times.
Two modes, 12 and 14. Each appears twice.
No mode. Every number appears once.
Blue. A mode works on words too, not only numbers.
9. The mode is the number that repeats, not how many times it repeats.

Part D — for 1 to 3, the mean first, then the median and the mode; for 4 to 7, the answer.

6 (mean). Median 6, mode 4.
20 (mean). Median 20, mode 16.
3 (mean). Median 3.0, no mode.
7. Yes, each 0 is a value, so you divide by 5, not 3.
7. In order it is 2, 4, 6, 8, 11, 15, and halfway between 6 and 8 is 7.
12. Five scores with a mean of 12 add to 60, and 10 + 14 + 9 + 15 = 48.
Yes. In 1, 2, 3, 4 the two middle numbers are 2 and 3, so the median is 2.5, which isn't in the set.

Part E — the answers.

a. 30.42 (365 ÷ 12) b. 31. In order, the 6th and 7th values are both 31. c. 31 is the mode. February, with 28 days, pulls the mean down.
a. 8 (48 ÷ 6) b. 7.5. In order it is 5, 6, 6, 9, 11, 11, and halfway between 6 and 9 is 7.5. c. There are two modes, 6 and 11.
99 (mean). The median is 112. The median describes her usual bowling better, because the one bad night pulls the mean down but doesn't move the middle.
The mode, because the store wants the size people actually buy most often. A mean like 7.6 isn't even a size you can order.

Part F — one correct answer, and what a good explanation says.

Answers vary. One that works is 4, 5, 5, 5, 6: the mode and median are 5, and the total is 25, so the mean is 25 ÷ 5 = 5. Numbers that balance evenly around the middle keep the mean on the median.
Answers vary. One is 1, 2, 3, 4, 20: the median is 3 and the mean is 30 ÷ 5 = 6. One very large number pulls the mean up but doesn't move the median.
Answers vary. A good answer puts the six numbers in order, takes the halfway number between the two middle values for the median, divides the total by 6 for the mean, and picks the measure that isn't thrown off by one unusual day.