AnswersConcepts in Probability and Statistics AComparing Mean and Median

Comparing Mean and Median Answers

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1
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Which statements are true about the median of a data set? Check all that apply.

A
The median isn’t affected much by one outlier.
B
The median is always affected by one outlier.
C
The median is the number in the middle on an ordered set of data.
D
To find the median, find the difference between the highest and lowest numbers.
E
To find the median of an even data set, find the average of the two middle numbers.
2
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Noah was asked to find the median of the following numbers. 115, 109, 117, 136, 127, 131Noah’s work is shown below. 109, 115, 117, 127, 131, 136What error, if any, did Noah make?

Question illustration
A
He forgot to put the numbers in order first.
B
He crossed off the high/low number pairs incorrectly.
C
He left out a number when putting the numbers in order.
D
He did not make any error.
3

Which set of data contains two outliers?

A
113, 115, 103, 114, 109, 111, 119
B
141, 151, 138, 142, 149, 140, 150
C
99, 113, 91, 104, 109, 114, 97
D
101, 135, 131, 99, 138, 136, 140
4

What is the median of this set of data? 1, 2, 5, 6, 9

A
1
B
5
C
8
D
9
5

Eva earned the following test scores in science:82, 100, 96, 90, 91Ms. Wade entered the next score as 0 because Eva was absent on test day and hadn’t had a chance to make up the test. Which statements are true based on the data? Check all that apply.

A
After adding the 0 test score, the mean would be the most appropriate measure of center to describe the data.
B
After adding the 0 test score, the mean would be affected.
C
After adding the 0 test score, the median would be the most appropriate measure of center to describe the data.
D
Before the missed test, Eva’s median score was 96.
E
Before the missed test, Eva’s median score was 91.
F
Before the missed test, Eva’s mean score was 91.8.
6

Jacob’s daily tips this work week were $99, $78, $58, $91, $90, and $68. Is Jacob correct in thinking that the median best represents how much money he makes in daily tips?

A
No, Jacob is not correct. The mean amount he makes is $82.67 in a day.
B
Yes, Jacob is correct. The mean amount he makes is $81.67 in a day.
C
No, Jacob is not correct. The median amount he makes is $86.00 in a day.
D
Yes, Jacob is correct. The median amount he makes is $84.00 in a day.
7

Mr. Malloy wants to make sure Amo and Javier get the best possible grade after five tests and can either give a grade based on the median or the mean. TestNumberAmo’s ScoresJavier’s Scores1976829297389654559259065What measure of center should Mr. Malloy use for Amo and for Javier for the best possible grade?

A
The teacher should use the mean for both Amo and Javier.
B
The teacher should use the median for both Amo and Javier.
C
The teacher should use the median for Amo and the mean for Javier.
D
The teacher should use the mean for Amo and the median for Javier.
8

Using the set of data below, which statements are true? Check all that apply. 13, 11, 16, 12, 42, 8

A
The mean of this data set is 17.
B
The median is 12.5.
C
The median is 14.5.
D
The mean is more affected by the outlier.
E
The median is more affected by the outlier.
F
The mean of this data set is 12.
9

Alicia received the following seven scores on her math assignments. 80, 90, 10, 75, 90, 95, 99Find the mean and median. Which measure of center best represents the data?

A
the mean
B
the median
C
both the mean and the median
D
neither the mean nor the median
10

Which set of data contains one outlier?

A
15, 19, 26, 51, 18, 21
B
22, 33, 31, 20, 28, 19
C
18, 20, 16, 22, 28, 26
D
27, 21, 31, 18, 21, 29
11

Which set of data does not contain any outliers?

A
113, 115, 103, 154, 109, 111, 119
B
141, 151, 111, 142, 149, 140, 150
C
99, 103, 91, 104, 109, 107, 97
D
131, 135, 131, 99, 138, 136, 140
12

Zahra was given two data sets, one without an outlier and one with an outlier. Data without an outlier: 15, 19, 22, 26, 29Data with an outlier: 15, 19, 22, 26, 29, 81How is the median affected by the outlier?

A
The outlier slightly affected the median.
B
The outlier made the median much higher than all the other values.
C
The outlier made the median much lower than all the other values.
D
The median is the exact same number in both data sets.
13

Sora was given two data sets, one without an outlier and one with an outlier. Data without an outlier: 108, 113, 105, 118, 124, 121, 109Data with an outlier: 108, 113, 105, 118, 124, 121, 109, 41How is the mean affected by an outlier?

A
The outlier did not affect the mean at all.
B
The outlier made the mean higher than all the other values.
C
The outlier made the mean lower than all the other values.
D
The mean is centered around all the other numbers in both sets of data.
14

What is the median of this set of data? 66, 51, 77, 68, 60, 75, 54, 80

A
29
B
64
C
66
D
67
15

Ari’s teacher says he may have his report grade based on either the mean or the median of his last six test scores. 88%, 73%, 97%, 76%, 90%, 80%Which measure of center would best represent Ari’s grade?

A
the mean
B
the median
C
both the mean and the median
D
neither the mean nor the median
16

Nicole received the following scores on her last 10 math assignments. 100, 88, 76, 78, 92, 94, 84, 98, 82, 90What is the Nicole’s median score?

A
24
B
88
C
89
D
93
17

Deepali was given two data sets, one without an outlier and one with an outlier. Data without an outlier: 15, 19, 22, 26, 29Data with an outlier: 15, 19, 22, 26, 29, 81How is the mean affected by an outlier?

A
The outlier did not affect the mean at all.
B
The outlier made the mean higher than all the other values.
C
The outlier made the mean lower than all the other values.
D
The mean is centered around all the other numbers in both sets of data.
18

Which lists the steps in the correct order to find the median of this data set?24, 16, 23, 30, 18, 29

A
1. Put the numbers in order.2. Cross off high/low pairs.3. Add the leftover numbers.4. Divide the sum by 2.
B
1. Put the numbers in order. 2. Cross of high/low pairs.
C
1. Cross off high/low pairs.2. Add the leftover numbers.3. Divide the sum by 2.
D
1. Cross of high/low pairs.
19

Peter’s teacher says he may have his report card percentage based on either the mean or the median and he can drop one test score if he chooses. 84%, 71%, 64%, 90%, 75%, 44%, 98%Which measure of center should Peter choose so he can have the highest percentage possible?

A
Peter should choose the mean after dropping one test score.
B
Peter should choose the mean without dropping one test score.
C
Peter should choose the median after dropping one test score.
D
Peter should choose the median without dropping one test score.

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