Deck 3: Measures of Central Tendency

Question 1

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

Answer 1

odd

Question 2

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

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

Answer 2

72

Question 3

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

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

Answer 3

mode

Question 4

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

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

Question 5

The median defines "central tendency" in terms of the

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

Question 6

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 7

The three commonly used measures of central tendency are

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

Question 8

The grades on a final exam for a statistics class are as follows: 25% As, 35% Bs, 30% Cs, 9% Ds and 1% Fs. The modal grade of the class is

A) A
B) B
C) C
D) D

Question 9

Which of the following correctly described the changing religious affiliation of the US since 1990?

A) The percentage of Americans who identify as Protestants has greatly increased
B) The percentage of Americans who identify as Protestants has stayed the same
C) The percentage of Americans with no religious affiliation has almost doubled
D) The percentage of Americans with no religious affiliation has greatly decreased

Question 10

What is the median of the following set of twelve grades? 55 60 62 67 70 72 74 76 77 85 90 95

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

Question 11

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 12

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 13

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 14

In a small seminar class, there were eight Protestants, four Catholics, three Jews, two Muslims, a Buddhist, and seven 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
D) the same as the median

Question 15

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 16

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 17

It is possible for a variable to have

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

Question 18

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

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

Question 19

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 20

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 21

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 22

The symbol X10 identifies

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

Question 23

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 24

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

Question 25

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

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

Question 26

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 27

The expression $\Sigma$ (Xi) directs us to find the

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

Question 28

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 29

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 30

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 31

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 32

The mean defines "central tendency" in terms of the

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

Question 33

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

A) mode
B) quartile
C) mean
D) proportion

Question 34

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 35

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 36

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

A) mode
B) quartile
C) mean
D) proportion

Question 37

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 38

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 39

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 40

A distribution of income for a sample of 45 people that consists of 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 41

The SPSS exercise in the text using state homicide rates for 1995 and 2012 showed

A) the average rate was higher in 2012
B) the rate was more positively skewed in 1995
C) the modal homicide rate fell dramatically
D) the median homicide rate was higher in 2012

Question 42

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 43

Which of the following is an accurate summary of the changing household incomes in the United States between 1967 and 2012?

A) Both the mean and median incomes rose but mean incomes increased more
B) The mean income fell while the median income rose
C) Both mean and median incomes fell
D) The median income fell while the mean income rose

Question 44

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 45

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 46

The text discusses some of the characteristics of the payrolls for two baseball teams. Which of the following correctly summarizes this comparison?

A) The Yankees had the lower average salary
B) The Red Sox had a lower median salary
C) Both payrolls showed a negative skew
D) The payroll for the Yankees showed a greater positive skew

Question 47

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 48

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

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