Deck 3: Measures of Central Tendency

Question 1

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 1

D

Question 2

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.

Answer 2

B

Question 3

A distribution of income for a sample of 45 people that included the presidents of the five largest corporations in the United States and 40 assembly line workers would be________.

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

Answer 3

C

Question 4

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 5

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 6

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 answer choices

Question 7

The mean can be calculated and used on all EXCEPT which of the following levels of measurement?

A) Interval-ratio
B) Nominal
C) Ordinal
D) The mean is valid for all of these choices.

Question 8

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 9

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 10

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

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

Question 11

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 12

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 answer choices

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

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 answer choices

Question 15

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 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 answer choices

Question 17

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 answer choices.

Question 18

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 19

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 20

The expressionΣ(Xi) directs us to find the________.

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

Question 21

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 answer choices

Question 22

The most appropriate measure of central tendency for gender would be the________.

A) median.
B) mode.
C) mean.
D) None of the answer choices

Question 23

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 24

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

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

Question 25

If one has data measured at the interval-ratio level, they can use which measure of central tendency?

A) Median
B) Mode
C) Mean
D) You can use any measure on interval-ratio data.

Question 26

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 answer choices

Question 27

The mode measures "central tendency" in terms of the most________.

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

Question 28

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

Question 29

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 30

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 31

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 32

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 33

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 34

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 35

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 36

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 37

In a small seminar class, there were eight students who identify as Protestant, four as Catholics, three as Jewish, two as Muslim, one as Buddhist, and seven students who have no religious affiliation. The mode for the variable religious affiliation is________.

A) eight.
B) undefined since the variable is nominal in level of measurement.
C) Protestant.
D) the same as the median.