Deck 3: Central Tendency.

Question 1

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

Answer 1

M = 6

Question 2

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

Answer 2

7

Question 3

What is the mean for the following scores? Scores: 4,6,14

A)12
B)8
C)7
D)6

Answer 3

8

Question 4

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 5

A population of N = 8 scores has ΣX = 40.What is the population mean?

A)320
B)20
C)5
D)0.2

Question 6

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 7

After 5 points are subtracted from every score,the sample mean is found to be M = 24.What was the mean for the original sample?

A)29
B)24
C)19
D)Cannot determine without knowing the number of scores in the sample

Question 8

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)Cannot be determined from the information provided

Question 9

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 10

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)Cannot be determined from the information given

Question 11

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

Question 12

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 13

What is the mean for the population of scores shown in the frequency distribution table? $$\begin{array} { c c } X & f \\\hline 5 & 2 \\4 & 1 \\3 & 3 \\2 & 2 \\1 & 2\end{array}$$

A)15/5 = 3
B)15/10 = 1.50
C)29/5 = 5.80
D)29/10 = 2.90

Question 14

A set of N = 8 scores has a mean of µ = 11.If 16 points are added to one of the scores,what is the new value for the population mean?

A)10
B)11
C)12
D)13

Question 15

A sample has a mean of M = 90.If each score in the sample is multiplied by 5,then what is the mean for the new distribution?

A)18
B)85
C)95
D)450

Question 16

A set of N = 4 scores has a mean of µ = 11.If 8 points are subtracted from one of the scores,what is the new value for the population mean?

A)13
B)11
C)10
D)9

Question 17

What is the mean for the population of scores shown in the frequency distribution table? $$\begin{array} { l l } \ X & \mathrm { f } \\\hline 5 & 1 \\4 & 2 \\3 & 3 \\2 & 4 \\1 & 2\end{array}$$

A)15/5 = 3
B)15/12 = 1.25
C)32/5 = 6.60
D)32/12 = 2.67

Question 18

What is the mean for the following sample of scores? Scores: 1,4,5,6

A)16
B)8
C)4.5
D)4

Question 19

A population with a mean of μ = 6 has ΣX = 54.How many scores are in the population?

A)N = 9
B)N = 27
C)N = 6×54 = 324
D)Cannot be determined from the information given

Question 20

My electric bills for June,July,and August last summer were $75,$75,and $150,respectively.What was the mean amount for the three bills?

A)$75
B)$100
C)$125
D)$150

Question 21

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 22

What is the value of the median for the following set of scores? Scores: 1,3,4,6,8,12,13,23,25,26

A)7
B)8
C)10
D)12.5

Question 23

A sample of n = 5 scores has a mean of M = 12.One new score is added to the sample,and the new mean is calculated to be M = 11.What is the value of new score?

A)X = 5
B)X = 6
C)X = 12
D)X = 60

Question 24

A population of N = 7 scores has a mean of µ = 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 25

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? $$\begin{array} { l l } X & f \\\hline 5 + & 2 \\4 & 3 \\3 & 2 \\2 & 1 \\1 & 1 \\0 & 1\end{array}$$

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

Question 26

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 27

One sample has n = 4 scores and M = 10.A second sample has n = 8 scores and M = 4.If the two samples are combined,what is the mean for the combined sample?

A)72/12 = 6
B)14/5 = 2.8
C)14/12 = 1.167
D)Cannot be determined with the information given

Question 28

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 6th 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 29

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

Question 30

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 31

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 32

What is the median for the following set of scores? Scores: 1,2,6,11,17

A)4
B)6
C)8.5
D)8

Question 33

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 34

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 35

What is the mode for the population of scores shown in the frequency distribution table? $$\begin{array} { c c } \mathrm { X } & \mathrm { f } \\5 & 1 \\4 & 2 \\3 & 3 \\2 & 4 \\1 & 2\end{array}$$

A)2
B)3
C)3.5
D)4

Question 36

What is the median for the set of scores shown in the frequency distribution table? $$\begin{array} { l l } \ X & \mathrm { f } \\\hline 5 & 1 \\4 & 1 \\3 & 2 \\2 & 3 \\1 & 4\end{array}$$

A)1
B)1.5
C)2
D)2.5

Question 37

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

Question 38

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 39

What is the median for the population of scores shown in the frequency distribution table? $$\begin{array} { l l } \ X& \mathrm { f } \\\hline 5 & 1 \\4 & 2 \\3 & 3 \\2 & 4 \\1 & 2\end{array}$$

A)2.5
B)3
C)3.5
D)4

Question 40

Which of the following statements is true?

A)It is possible for a distribution to have two means.
B)It is possible for a distribution to have two medians.
C)It is possible for a distribution to have two modes.
D)It is possible for a distribution to have two medians or two modes.

Question 41

For a perfectly symmetrical distribution with µ = 30,what is the mode?

A)30
B)Greater than 30
C)Less than 30
D)Cannot be determined from the information given

Question 42

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 43

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 44

What is the preferred measure of central tendency for scores measured on an ordinal scale?

A)The mean
B)The median
C)The mode
D)Central tendency cannot be determined for ordinal data

Question 45

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

Question 46

For the scores in the following frequency distribution table,the mean is M = 3.
$$\begin{array} { l l } X & f \\\hline 4 & 1 \\3 & 4 \\2 & 2\end{array}$$

Question 47

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

Question 48

What is the most likely shape for a distribution with a mean of 40 and a mode of 45?

A)Symmetrical
B)Positively skewed
C)Negatively skewed
D)Either positively or negatively skewed

Question 49

Under what circumstances is the median likely to produce a better measure of central tendency than the mean?

A)With a symmetrical distribution
B)With an extremely skewed distribution
C)When the data consist of nominal measurements
D)When the data are numerical scores from an interval or a ratio scale

Question 50

For a positively skewed distribution with a mode of X = 20 and a median of 25,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 51

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

Question 52

For a perfectly symmetrical distribution,which relationship is always true?

A)Mean = median
B)Mean = mode
C)Median = mode
D)Mean = median = mode

Question 53

For a positively 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 54

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 55

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

Question 56

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 57

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 58

A sample has n = 7 scores with a mean of M = 9.If one individual with a score of
X = 3 is removed from the sample,the new mean will be M = 10.

Question 59

A sample has a mean of M = 40.If a new score of X = 35 is added to the sample,then the sample mean would increase.

Question 60

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 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

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 63

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

Question 64

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

Question 65

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

Question 66

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

Question 67

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

Question 68

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

Question 69

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

Question 70

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

Question 71

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

Question 72

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

Question 73

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

Question 74

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

Question 75

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

Question 76

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

Question 77

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 78

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

Question 79

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 80

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.