Deck 3: Measures of Central Tendency

Question 1

It is possible for a variable to have

A)one mode.
B)many modes.
C)no mode.
D)all of the above

Answer 1

all of the above

Question 2

The mode measures "central tendency" in terms of the most

A)common score.
B)central case.
C)important score.
D)average case.

Answer 2

common score.

Question 3

What measure of central tendency would be most appropriate to summarize data about the color of movie stars' eyes?

A)median
B)mode
C)mean
D)none of the above

Answer 3

mode

Question 4

In a small seminar class,there were eight Protestants,four Catholics,three Jews,two Muslims,a Buddhist,and eight students with no religious affiliation ("Nones").The mode for this variable is

A)eight.
B)undefined since the variable is nominal in level of measurement.
C)Protestant and "None."
D)the same as the median.

Question 5

The median represents the score that is

A)half of the sum of the other scores.
B)the most common or frequent.
C)in the middle.
D)midway between the highest and lowest scores.

Question 6

If the scores on a variable are 11,14,18,19,20,and 25,the median is

A)3.
B)18.
C)18.5.
D)19.

Question 7

For ordinal level variables,the most appropriate measure of central tendency is generally

A)the mode.
B)the median.
C)the mean.
D)none of the above

Question 8

The median is the score of the middle case when the number of cases is

A)odd.
B)even.
C)more than 20.
D)less than 20.

Question 9

What is the median of the following set of eleven grades?
55 $\quad$ 60 $\quad$ 62 $\quad$ 67 $\quad$ 70 $\quad$ 72 $\quad$ 75 $\quad$ 76 $\quad$ 77 $\quad$ 85 $\quad$ 95

A)Since these are interval-ratio scores,the median cannot be found.
B)70
C)71
D)72

Question 10

The median defines "central tendency" in terms of the

A)most common score.
B)central case.
C)most likely or probable score.
D)largest score.

Question 11

The three commonly used measures of central tendency are

A)more,median,and mean.
B)percentage,midpoint,and mean.
C)mode,midpoint,and ratio.
D)median,rate,and mode.

Question 12

The mode should be used to measure central tendency when the level of measurement of the variable is

A)nominal.
B)ordinal.
C)interval-ratio.
D)all of the above

Question 13

The median cannot be found for variables measured at the nominal level because

A)there is no central tendency.
B)the scores cannot be ranked or ordered.
C)all of the cases are representative.
D)the distribution is skeweD.

Question 14

The most appropriate measure of central tendency for gender would be the

A)median.
B)mode.
C)mean.
D)none of the above

Question 15

In a ranked list of 25 scores,the median is the score of

A)the 12th case.
B)the 13th case.
C)the average of the scores of the 12th and 13th cases.
D)the average of all of the scores.

Question 16

What is the median of the following set of twelve grades?
55 $\quad$ 60 $\quad$ 62 $\quad$ 67 $\quad$ 70 $\quad$ 72 $\quad$ 75 $\quad$ 76 $\quad$ 77 $\quad$ 85 $\quad$ 95

A)Since these are interval-ratio scores,the median cannot be found.
B)72
C)73
D)74

Question 17

The three commonly used measures of central tendency (mode,median,and mean)

A)will always have the same value.
B)will always fall in the same order: the mean will have the highest value,followed by the median and the mode.
C)define "typical" or "average" in different ways and will usually have different values.
D)will always fall in the same order: the mean will have the lowest value,the median will always be in the middle and the mode will have the highest value.

Question 18

If the scores of an even number of cases are arranged from high to low,the median is

A)the middle score.
B)the average of the two middle scores.
C)the average of the highest and lowest scores.
D)the same as the mode.

Question 19

If the scores on a variable are 11,14,18,20,and 25,the median is

A)3.
B)16.
C)18.
D)19.

Question 20

The purpose of measures of central tendency is to describe what value of a distribution of scores is

A)the most typical or representative.
B)the most surprising or unexpected.
C)the most significant or important.
D)all of the above

Question 21

If you subtracted the mean from each score in a distribution and added the results,the sum would be

A)zero.
B)less than zero.
C)a minimum.
D)the mode.

Question 22

In a positively skewed distribution the mean is

A)equal in value to the median.
B)greater in value than the median.
C)less in value than the median.
D)either a or b,depending on the value of the mode.

Question 23

In any distribution,the mean and the median will have the same value when the distribution is

A)symmetrical.
B)positively skewed.
C)negatively skewed.
D)all of the above

Question 24

If you changed ONLY the highest score in a distribution of 5 scores,which of the following measure of central tendency would be affected?

A)the mean
B)the median
C)the mode
D)all of the above

Question 25

The mean defines "central tendency" in terms of the

A)most common score.
B)typical case.
C)average score.
D)most likely score.

Question 26

If you subtracted the mean from each score in a distribution,squared the differences,and then added the squared differences,the sum would be

A)zero.
B)less than zero.
C)a minimum.
D)a maximum.

Question 27

If a distribution of test scores has a mean of 70 and a median of 63,the distribution has

A)a few very low scores.
B)a mode of 67.
C)a negative skew.
D)a positive skew.

Question 28

The expression S(X_i)directs us to find the

A)average of the scores.
B)middle score.
C)sum of the scores.
D)median.

Question 29

For variables measured at the interval-ratio level,the preferred measure of central tendency would be the

A)mode.
B)quartile.
C)mean.
D)decile.

Question 30

What is the mean of the following scores?
13 $\quad$ 18 $\quad$ 23 $\quad$ 35 $\quad$ 41

A)23
B)24
C)26
D)28

Question 31

The most appropriate measure of central tendency for the variable age (measured in years)would be the

A)mode.
B)quartile.
C)mean.
D)decile.

Question 32

If a distribution of test scores has a mean of 70 and a median of 80,the distribution has

A)a few very high scores.
B)a mode of 75.
C)a negative skew.
D)a positive skew.

Question 33

The symbol X₁₀ identifies

A)the first decile.
B)the tenth score.
C)the mode.
D)any score which has a value one tenth of the mean.

Question 34

On a survey,age was divided into three categories:
1)Younger than 18
2)18 to 21
3)Older than 21
The researcher computed the mean age of her respondents by adding up the scores (the 1s,2s,and 3s)and then dividing by the number of cases.This was a mistake because the data are

A)only nominal and shouldn't be treated as ordinal.
B)continuous and shouldn't be treated as discrete.
C)interval-ratio.No mistake has been made.
D)ordinal and shouldn't be treated as interval-ratio.

Question 35

Deciles,quartiles,and percentiles divide a distribution of scores into,respectively,

A)ones,twos,and threes.
B)fourths,fifths,and thirds.
C)tens,twenties,and forties.
D)tens,quarters,and hundredths.

Question 36

To locate the 6th decile,we would first multiply the number of cases (N)by

A).06.
B).60.
C)6.00.
D)the value of the median minus ten.

Question 37

The sum of the differences between the scores of a distribution and the mean of the scores is always

A)0.
B)1.
C)the same as the number of cases.
D)none of the above

Question 38

The fourth decile would be at the same location as

A)the second quartile.
B)the fourth percentile.
C)the fortieth percentile.
D)the fourth quartile.

Question 39

Which measure of central tendency is like "a fulcrum that exactly balances all of the scores?"

A)mode
B)median
C)mean
D)none of the above

Question 40

Which measure of central tendency is affected by every score in the distribution?

A)the mean
B)the median
C)the mode
D)all of the above

Question 41

To compute a mean for scores that have been grouped into a frequency distribution,we assume that the scores in each interval are

A)spread evenly across the interval.
B)twice the value of the next lower interval.
C)located at the lower real limit of the interval.
D)located at the midpoint of the interval.

Question 42

A researcher is preparing a report and wants to select a measure of central tendency that shows the most common score in a particular distribution.Which statistic should she select?

A)mode
B)median
C)mean
D)none of the above

Question 43

When interval-ratio data are badly skewed,the appropriate measure of central tendency is the

A)mode.
B)median.
C)mean.
D)first quartile.

Question 44

Which of the following correctly matches the level of measurement of a variable with the preferred measure of central tendency?

A)nominal ...mean
B)ordinal ...mode
C)interval-ratio ...mode
D)ordinal ...median

Question 45

You have come across some statistics regarding the average cost of new housing in your city and a nearby city over the past few years.Write a paragraph summarizing these statistics.

Question 46

An instructor is preparing a report showing mid-semester grades and notes that the mean,median,and mode are all exactly 76.00.What can she conclude?

A)The distribution of grades is unskewed.
B)There is a negative skew in the distribution (a few students have very low grades. )
C)There is a positive skew in the distribution (a few students have very high grades).
D)all of the above

Question 47

A math professor is wondering if students today are better or worse than in the past.He has given the same final to this year's class that he gave ten years ago.Compute mean,median,and mode for both classes and write a paragraph summarizing the differences.

Question 48

Income distributions almost always have a positive skew (since there are only a few very wealthy people).Therefore,the preferred measure of central tendency for this variable would be the

A)mode.
B)median.
C)mean.
D)none of the above

Question 49

To compute a median for scores that have been grouped into a frequency distribution,we assume that the scores in each interval are

A)spaced evenly across the interval.
B)located at the upper real limit of the interval.
C)located at the lower stated limit of the interval.
D)located at the midpoint of the interval.

Question 50

A distribution of income for a sample of 45 people that included the presidents of the five largest corporations in the United States and forty assembly line workers would be

A)unskewed.
B)negatively skewed.
C)positively skewed.
D)symmetrical.

Question 51

In a campaign debate over the level of prosperity in the state,the incumbent governor says: "average income is $53,000." His opponent responds "the average citizen earns only $38,000." Both statements are true.This is possible because

A)the governor is citing the median.
B)the opponent is using the mode.
C)the opponent is using the mean.
D)the governor is using the mean.