Deck 3: Central Tendency

Question 1

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

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

Answer 1

?29/10 = 2.90

Question 2

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 = 3
B)​X = 5
C)​X = 10
D)​X = 15

Answer 2

​X = 15

Question 3

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)3​
B)​27
C)​30
D)​33

Answer 3

​33

Question 4

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 5

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)​between 50 and 52

Question 6

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)​Adding a score equal to the mean.

Question 7

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

A)​20
B)​10
C)​5
D)​4

Question 8

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

A)​The sample mean will increase a little.
B)​The sample mean will decrease.
C)​The sample mean will remain the same.
D)​The sample mean will increase substantially.

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

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 weighted mean for the combined sample?​

A)​70/4 = 17.5
B)​70/6 = 11.7
C)​70/10 = 7.0
D)​10/5=2.0

Question 11

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)​X=10

Question 12

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

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

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)​3
C)​21
D)​63

Question 14

A sample has a mean of M = 40.If 10 points are added to one of the scores,what happens to the sample mean?​

A)​it is unchanged
B)​it increases
C)​it decreases a little
D)​it decreases substantially

Question 15

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

A)180​
B)​30
C)​15
D)​5

Question 16

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

A)​N = 6/42 = 1/7
B)​N = 42/6 = 7
C)​N=42
D)​N = 6*42 = 252

Question 17

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)​The mean is M=10.

Question 18

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)​5²=25

Question 19

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

A)​3
B)​6
C)​7
D)​10.5

Question 20

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 weighted mean for the combined set of scores?​

A)​4.8
B)​9.6
C)​10.0
D)​19.2

Question 21

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)​weighted mean

Question 22

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)​It is equal to the mean.

Question 23

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)​mean
B)​median
C)​mode
D)​weighted mean

Question 24

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 25

A distribution with two modes is said to be:​

A)​two modal
B)​minor modal
C)​bimodal
D)​main modal

Question 26

For a bell-shaped distribution with µ = 30,what is the most probable value for the mode?​

A)​30
B)​greater than 30
C)​less than 30
D)​0

Question 27

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)​equal to 25
C)​between 20 and 25
D)​less than 20

Question 28

Which of the following statements is true for a distribution of data points?​

A)​75% of the data points are above the median.
B)​50% of the scores are above the median.
C)​60% of the scores are below the median.
D)​95% of the data points are above the median.

Question 29

What is the value of the median for the following set of scores? Scores: 1,3,4,6,7,8,12,23​

A)​6
B)​6.5
C)​7
D)​8

Question 30

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=11.7
B)​66/6=11.0
C)​70/7=10.0
D)​66/7=9.4

Question 31

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 32

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 = 7.0
B)​M = 8.0
C)​M = 8.8
D)​M=11.0

Question 33

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 34

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

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

Question 35

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

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

Question 36

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??? $$\begin{array} { c c } \mathrm { X } & \mathrm { f } \\5 \text { or more } & 2 \\4 & 3 \\3 & 2 \\2 & 1 \\1 & 1 \\0 & 1\end{array}$$ ?

A)mean?
B)?median
C)?mode
D)?weighted mean

Question 37

Which of the following statements is true for a distribution of scores?​

A)​No score is exactly equal to the mean.
B)​No score is exactly equal to the median.
C)​At least one score is exactly equal to the mode.
D)​At least one score is equal to the median.

Question 38

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)​bimodal

Question 39

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

A)​greater than 30
B)​30
C)​20 to 29.5
D)​less than 20

Question 40

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)​20
C)​less than 20
D)​0

Question 41

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

Question 42

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 43

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

Question 44

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 sample mean for the combined sample will be greater than 55.​

Question 45

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 46

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

Question 47

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 48

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

Question 49

A sample with modes of 4,8,and 10 is said to be multimodal.​

Question 50

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

Question 51

Every dataset will have a mode.​

Question 52

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

Question 53

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

Question 54

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 55

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

Question 56

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

Question 57

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

Question 58

The major mode occurs with less frequency than the minor mode.​

Question 59

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 60

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 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

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

Question 63

Means that are on an interval or ratio scale are best shown graphically on a line graph.​

Question 64

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

Question 65

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

Question 66

Figure 3.1
Find the mean,the median,and the mode for the set of scores in the accompanying frequency distribution histogram,Figure 3.1.​

Question 67

Explain why it is necessary to have more than one standard procedure for defining and measuring central tendency.​

Question 68

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

Question 69

Compute the mean,median,and mode for the set of scores shown in the following frequency distribution table.​

Question 70

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

Question 71

What is the purpose for obtaining a measure of central tendency?​

Question 72

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

Question 73

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

Question 74

A set of n = 6 scores has a mean of M = 10.Another set of scores has n = 4 and M = 15.If these two sets of scores are combined,what is the weighted mean for the combined group?​

Question 75

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