Deck 3: Central Tendency

Question 1

A population of N = 10 scores has a mean of μ = 6.After one score is removed, the mean is found to be M = 5.What is the value of the score that was removed?

A)X = 10
B)X = 5
C)X = 3
D)X = 15

Answer 1

D

Question 2

A sample has a mean of M = 86.If one new person is added to the sample, what effect will it have on the sample mean?

A)The sample mean will increase.
B)The sample mean will decrease.
C)The sample mean will remain the same.
D)cannot be determined from the information given

Answer 2

D

Question 3

One sample with n = 4 scores has a mean of M = 12, and a second sample with n = 6 scores has a mean of M = 8.If the two samples are combined, what is the mean for the combined set of scores?

A)4.8
B)9.6
C)10.0
D)19.2

Answer 3

B

Question 4

A population with a mean of μ = 6 has ΣX = 42.How many scores are in the population?

A)N = 7
B)N = 252
C)N = 6/42 = 1/7
D)cannot be determined from the information given

Question 5

A set of N = 10 scores has a mean of µ = 50.If 20 points are added to one of the scores, what is the new value for the population mean?

A)50
B)51
C)52
D)70

Question 6

A sample of n = 5 scores has a mean of M = 8.One new score is added to the sample and the new mean is calculated to be M = 9.What is the value of new score?

A)X = 5
B)X = 9
C)X = 14
D)X = 54

Question 7

Which of the following actions will always change the value of the mean?

A)changing the value of one score
B)adding a new score to the distribution
C)removing a score from the distribution
D)All 3 of the other choices are correct.

Question 8

A population of N = 6 scores has ΣX = 30.What is the population mean?

A)180
B)30
C)15
D)5

Question 9

A sample of n = 6 scores has a mean of M = 5.One person with a score of X = 12 is added to the distribution.What is the mean for the new set of scores?

A)M = 5
B)M = 6
C)M = 7
D)M = 8

Question 10

A sample of n = 5 scores has a mean of M = 12.What is ΣX for this sample?

A)12/5 = 2.40
B)5/12 = 0.417
C)5(12) = 60
D)cannot be determined from the information given

Question 11

For the population of scores shown in the frequency distribution table, the mean is ____.

Question 12

What is the mean for the following sample of scores? Scores: 1, 4, 5, 10

A)20
B)10
C)5
D)4

Question 13

After every score in a sample is multiplied by 3, the mean is calculated and found to be M = 21.What was the mean for the original scores?

A)7
B)21
C)63
D)cannot be determined from the information given

Question 14

What is the mean for the population of scores shown in the frequency distribution table?

Question 15

A distribution of scores has a mean of μ = 50.One new score is added to the distribution and the new mean is found to be μ = 48.From this result you can conclude that the new score was _____.

A)greater than 50
B)less than 50
C)equal to 48
D)cannot answer from the information given

Question 16

In a sample of n = 6 scores, the smallest score is X = 3, the largest score is X = 10, and the mean is M = 6.If the largest score is changed from X = 10 to X = 22, then what is the value of the new mean?

A)The mean is still M = 6
B)The mean is M = 7
C)The mean is M = 8
D)impossible to determine from the information given

Question 17

What is the mean for the following scores? Scores: 1, 6, 14

A)3
B)6
C)7
D)10.5

Question 18

A sample has a mean of M = 40.If 10 points are added to one of the scores, what is the new value for the sample mean?

A)still 40
B)41
C)50
D)cannot be determined from the information given

Question 19

A sample of n = 8 scores has a mean of M = 10.After one score is removed from the sample, the mean for the remaining score is found to be M = 11.What was the score that was removed?

A)X = 3
B)X = 7
C)X = 8
D)impossible to determine from the information provided

Question 20

A population has a mean of µ = 30.If 3 points are added to each score, what is the mean for the new distribution?

A)27
B)30
C)33
D)cannot be determined from the information given

Question 21

A sample of n = 4 scores has a mean of M = 8.If one new score with a value of X = 3 is added to the sample, what will be the value for the new mean?

A)M = 7
B)M = 8
C)M = 8.75
D)cannot be determined with the information provided

Question 22

A distribution is positively skewed.Which is the most probable order, from smallest to largest, for the three measures of central tendency?

A)mean, median, mode
B)mode, median, mean
C)mean, mode, median
D)median, mean, mode

Question 23

Which of the following statements cannot be true for a distribution of scores?

A)No one has a score exactly equal to the mean.
B)No one has a score exactly equal to the median.
C)No one has a score exactly equal to the mode.
D)All of the other options are false statements.

Question 24

Which of the following statements cannot be true for a distribution of scores?

A)60% of the scores are above the mean.
B)60% of the scores are above the median.
C)60% of the scores are above the mode.
D)All of the other options are false statements.

Question 25

A researcher measures eye color for a sample of n = 50 people.Which measure of central tendency would be appropriate to summarize the measurements?

A)mean
B)median
C)mode
D)any of the three measures could be used

Question 26

One sample has n = 4 scores and M = 10.A second sample has n = 6 scores and M = 5.If the two samples are combined, then what is the mean for the combined sample?

A)70/4 = 17.5
B)70/6 = 11.67
C)70/10 = 7
D)cannot be determined with the information given

Question 27

What is the median for the population of scores shown in the frequency distribution table?

Question 28

For a perfectly symmetrical distribution with µ = 30, what is the most probably value for the mode?

A)30
B)greater than 30
C)less than 30
D)cannot be determined from the information given

Question 29

One item on a questionnaire asks students how many times in a typical week they eat at a fast-food restaurant.The responses for a sample of n = 10 students are summarized in the frequency distribution.What is the best measure of central tendency for these data?

Question 30

What is the median for the following set of scores?

A)4
B)6 Scores: 1, 2, 6, 11, 17
C)8.5
D)8

Question 31

In a population of N = 6, five of the individuals all have scores that are exactly 1 point above the mean.From this information, what can you determine about the score for the sixth individual?

A)It is also above the mean by 1 point.
B)It is below the mean by 1 point.
C)It is below the mean by 5 points.
D)There is not enough information to describe the 6th score.

Question 32

A population of N = 7 scores has a mean of $\mu$ = 10.If one score with a value of X = 4 is removed from the population, what is the value for the new mean?

A)70/6
B)66/7
C)66/6 = 11
D)cannot be determined from the information given

Question 33

For a negatively skewed distribution with a mode of X = 25 and a median of 20, what is the most likely value for the mean?

A)greater than 25
B)less than 20
C)between 20 and 25
D)cannot be determined from the information given

Question 34

What is the mode for the following sample of n = 8 scores? Scores: 0, 1, 1, 1, 2, 2, 3, 3

A)1
B)1.5
C)13/8 = 1.625
D)3

Question 35

A population of scores has a mean of µ = 26, a median of 23, and a mode of 22.What is the most likely shape for the population distribution?

A)symmetrical
B)positively skewed
C)negatively skewed
D)cannot be determined from the information given

Question 36

For a negatively skewed distribution with a mean of M = 20, what is the most probable value for the median?

A)greater than 20
B)less than 20
C)20
D)cannot be determined from the information given

Question 37

What is the value of the median for the following set of scores?

A)6
B)6.5 Scores: 1, 3, 4, 6, 7, 8, 12, 23
C)7
D)64/8 = 8

Question 38

A researcher is measuring the amount of time needed to solve a set of anagrams for a sample of n = 15 students.However, one of the participants fails to solve the problems so the researcher has an undetermined score.What is the best measure of central tendency for these data?

A)the mean
B)the median
C)the mode
D)Central tendency cannot be determined for these data.

Question 39

For a perfectly symmetrical distribution with a median of 30, what is the value of the mean?

A)30
B)greater than 30
C)less than 30
D)cannot be determined from the information given

Question 40

What is the mode for the population of scores shown in the frequency distribution table?

Question 41

A sample of n = 7 scores has a mean of M = 5.After one new score is added to the sample the new mean is calculated to be M = 6.The new score was X = 13.

Question 42

A sample of n = 6 scores has ΣX = 48.This sample has a mean of M = 8.

Question 43

A sample has a mean of M = 40.If a new score of X = 55 is added to the sample, then the sample mean would increase.

Question 44

If a sample has an odd number of scores, at least one individual will have a score exactly equal to the median.

Question 45

A sample of n = 10 scores has a mean of 50.A second sample has n = 5 scores and
M = 60.If the two samples are combined, the combined sample mean will be greater than 55.

Question 46

In a sample of n = 3 scores, two scores are each below the mean by 2 points.The third score is above the mean by 4 points.

Question 47

A sample has n = 7 scores with a mean of M = 7.If one individual with a score of
X = 1 is removed from the sample, the new mean will be M = 8.

Question 48

A sample of n = 8 scores has a mean of M = 20.After one score is removed from the sample, the mean is calculated to be M = 23.The removed score must have a value greater than 20.

Question 49

The mean is considered to be the "balance point" for a distribution because exactly half of the scores are located above the mean and exactly half are below the mean.

Question 50

A sample of n = 6 scores has a mean of M = 9.If one individual with a score of X = 4 is removed from the sample, the new mean will be M = 10.

Question 51

A sample with a mean of M = 20 has ΣX = 120.There are n = 6 scores in the sample.

Question 52

Adding a new score to a distribution will always change the value of the mean.

Question 53

A student takes a 10-point quiz each week in statistics class.If the student's quiz scores for the first three weeks are 2, 6, and 10, then the mean score is M = 9.

Question 54

For any distribution of scores at least one individual will have a score exactly equal to the mean.

Question 55

A sample of n = 8 scores has a mean of M = 16.For this sample ΣX = 2.

Question 56

For a distribution with one or two extreme scores, the median is usually a more representative value than the mean.

Question 57

For a 100-point exam, a score of X = 65 is definitely above the median.

Question 58

For the scores in the following frequency distribution table, the mean is M = 3.

Question 59

Changing the value of a score in a distribution will always change the value of the mean.

Question 60

After adding 6 points to every score in a sample, the new mean is found to be M = 18.The mean for the original sample was M = 24.

Question 61

A distribution of scores has a mean of 50, a median of 53, and a mode of 56.Based on this information it appears that the distribution is negatively skewed.

Question 62

For a set of scores measured on an ordinal scale, the median is the preferred measure of central tendency.

Question 63

A sample has n = 5 scores: 2, 4, 5, 8, and 11.The median for the sample is 6.5.

Question 64

It is possible to have a distribution of scores where no individual has a score exactly equal to the mode.

Question 65

For a negatively skewed distribution, the mean usually has a larger value than either the median or the mode.

Question 66

It is possible for a distribution to have more than one mode.

Question 67

For a severely skewed distribution, the median often provides a better measure of central tendency than the mean.

Question 68

If a negatively skewed distribution has a mean of 50, then the median and the mode are both probably greater than 50.

Question 69

It is impossible for the value of the mode to be greater than the value of the mean.

Question 70

There are situations for which it is either impossible to compute a mean or the mean does not provide a central, representative value.