Deck 3: Measures of Central Tendency

Question 1

Measures of central tendency

A) indicate how much the scores vary from one another.
B) describe the most typical score in an entire distribution.
C) indicate the most frequently occurring score in a distribution of scores.
D) all of the above are true.

Answer 1

B

Question 2

Which measure of central tendency specifies the score value with the highest frequency?

A) mode
B) median
C) mean
D) standard deviation

Answer 2

A

Question 3

Which measure of central tendency is defined as the middle point in a distribution with half of the scores above it and half of the scores below it?

A) mode
B) median
C) mean
D) standard deviation

Answer 3

B

Question 4

All of the following are true of the mode, except that it

A) ignores all other scores.
B) lacks stability.
C) is the frequency of the highest score.
D) can change dramatically if one score changes.

Question 5

What is the mode for the following set of scores: 6, 8, 2, 6, 7, 9, 6?

A) 9
B) 9
C) 6.5
D) 6

Question 6

What is the median for the following set of scores: 2, 4, 2, 8, 4, 2, 5, 3?

A) 2
B) 3.5
C) 4
D) 8

Question 7

What is the median for the following set of scores: 14, 11, 16, 11, 9, 18, 12?

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

Question 8

What is the mean for the following set of scores: 5, 10, 10, 15, 5?

A) 9
B) 10
C) 15
D) 5

Question 9

If you are working with a grouped frequency distribution, the mode would be

A) the class interval with the greatest frequency.
B) the beginning value of the class interval with the greatest frequency.
C) the upper limit of the class interval with the greatest frequency.
D) the mid-point of the class interval with the greatest frequency.

Question 10

Four people in a sample scored 6; another person scored 8; and one other person scored 10. What is the mean?

A) 6
B) 7
C) 8
D) 7.5

Question 11

The value of the mean will change in response to

A) adding another score to the data set.
B) removing a score from the data set.
C) changing the value of a score from the data set.
D) all of the above.

Question 12

Changing the value of one of the scores in a data will always affect the

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

Question 13

In a set of scores, at least one person will have a score that is equal to

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

Question 14

If a set of scores has two modes it will result in a distribution that is

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

Question 15

The symbol for the mean of a population is ________.

A) M
B) μ
C) f
D) σ

Question 16

If you know that the mean of a distribution is 85 and that the median is 95, you also know that the distribution is

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

Question 17

If you know that the mean of a distribution is 50 and that the mode is 25, you also know that the distribution is

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

Question 18

Which of the following statements is true of the median?

A) It takes all score values into consideration.
B) It is biased by extreme scores in the distribution.
C) It may not be an actual score.
D) It is the measure of central tendency used most often in statistics.

Question 19

The formula method for determining the median is used when working from

A) a grouped frequency distribution.
B) a simple frequency distribution.
C) a distribution table with a column for P.R.
D) a distribution table with a column for Rel. f.

Question 20

When using the formula method for determining the median, which of the following is NOT required?

A) LL
B) i
C) cf_below
D) ∑X

Question 21

If you are working with scores from an actual population, the number of scores would be symbolized by ______ and the mean would be symbolized as _______.

A) N; M
B) N; μ
C) n; M
D) n; μ

Question 22

To determine the mean for a set of scores,

A) start by dividing the distribution of scores in half.
B) start by looking for the most common score.
C) start by adding up all of the scores in the distribution.
D) multiply the sum of the scores by the total number of scores.

Question 23

If you are calculating the mean for scores that have been arranged into a simple frequency distribution, what additional step has to be taken?

A) ∑fX
B) ∑f
C) ∑cf
D) ∑N

Question 24

To determine which measure of central tendency to use, we need to identify

A) the independent variable(s) and dependent variable.
B) the shape of the distribution and the scale of measurement.
C) the extraneous variables.
D) the standard deviation.

Question 25

How would you describe the shape of the distribution for the following set of scores: 10, 10, 10, 20, 20, 20, 20, 20, 30, 30, 30, 30, 30, 50, 60, 60, 70, 80?

A) symmetrical
B) positively skewed
C) negatively skewed
D) bimodal

Question 26

How would you describe the shape of the distribution for the following set of scores: 10, 20, 20, 30, 30, 30, 40, 40, 40, 40, 40, 50, 50, 50, 50, 50, 60, 60, 60, 60, 60, 70, 70, 70, 70, 80, 80, 80?

A) symmetrical
B) positively skewed
C) negatively skewed
D) rectangular

Question 27

How would you describe the shape of the distribution for the following set of scores: 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8?

A) symmetrical
B) positively skewed
C) negatively skewed
D) bimodal

Question 28

Which measure of central tendency is never influenced by extreme scores in the tails of the distribution?

A) mode
B) median
C) mean
D) standard deviation

Question 29

The symbol "μ" represents

A) the mode.
B) the median.
C) the sample mean.
D) the population mean.

Question 30

Which of the following statements is NOT true of the sample mean?

A) It is an unbiased estimate of the population mean.
B) It takes every score value into consideration.
C) It is a biased estimate of the population mean.
D) It can be used for further statistical operations.

Question 31

Which of the following statements is true of the sample mean?

A) It systematically overestimates the value of the population mean.
B) It systematically underestimates the value of the population mean.
C) It cannot be used to estimate the value of the population mean.
D) It is an unbiased estimate of the population mean.

Question 32

The only measure of central tendency that can be used for variables measured on a nominal scale is the

A) mode.
B) median.
C) mean.
D) standard deviation.

Question 33

The mode can be determined for which scales of measurement?

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

Question 34

The median can be used for any of the scales of measurement, except

A) nominal.
B) ordinal.
C) interval.
D) ratio.

Question 35

The mean can be determined for which scale(s) of measurement?

A) nominal or ordinal
B) interval or ratio
C) nominal or interval
D) ordinal or interval

Question 36

A naturalist categorizes plants into different species. Since the categories represent a _______________ scale, the appropriate measure of central tendency would be _______________.

A) ordinal; median
B) ordinal; mode
C) nominal; mode
D) nominal; median

Question 37

The preferred measure of central tendency in a skewed distribution is

A) the standard deviation.
B) the mode.
C) the median.
D) the mean.

Question 38

The preferred measure of central tendency in a normally shaped distribution is

A) the standard deviation.
B) the mode.
C) the median.
D) the mean.

Question 39

In a skewed distribution, the location of the ______________ will be towards the tail of the distribution in the direction of the extreme scores.

A) mean
B) median
C) mode
D) standard deviation

Question 40

In a negatively skewed distribution, the mean will be

A) towards the low scores.
B) towards the high scores.
C) in the middle of the distribution.
D) between the mode and the median.

Question 41

In a positively skewed distribution, the mode will be

A) towards the low scores.
B) towards the high scores.
C) in the middle of the distribution.
D) between the median and the mean.

Question 42

In a positively skewed distribution, the median will be

A) toward the right of the mean.
B) between the mode and the mean.
C) toward the right tail of the distribution.
D) toward the left of the mode.

Question 43

The mean, mode, and median will all be in the same location in a

A) positively skewed distribution.
B) negatively skewed distribution.
C) normally shaped distribution.
D) bimodal distribution.

Question 44

If a distribution is positively skewed, the smallest value will be

A) the mode.
B) the median.
C) the mean.
D) the standard deviation.

Question 45

An unscrupulous CEO of a large tech company is recruiting for new hires. The top few executives in the company earn huge salaries, but most of the other employees earn salaries that are quite a bit lower. Since he wants to make a good impression, which measure of central tendency does the CEO report to the potential new hires?

A) mode
B) median
C) mean
D) standard deviation

Question 46

Which measure of central tendency should a researcher use to describe the most representative gender in a study?

A) median
B) mode
C) mean
D) standard deviation

Question 47

A researcher using the amount of time to complete a task should use which measure of central tendency?

A) the mean if the distribution is skewed
B) the median if the scores are normally distributed
C) the mean if the distribution is symmetrical
D) the mode if the distribution is skewed

Question 48

Briefly define the following terms:
a. Central tendency
b. Mode
c. Median
d. Mean

Question 49

Why is the mode problematic as a measure of central tendency?

Question 50

What are the advantages of using the mean as a measure of central tendency?

Question 51

If a distribution is severely skewed, is the mean or the median the preferred measure of central tendency? Why?

Question 52

If a distribution is positively skewed, the a) ______________ will have the highest score value and the b) ______________ will have the lowest score value. If a distribution is negatively skewed, the c) ______________ will have the highest score value and the d) ______________ will have the lowest score value.

Question 53

If a distribution is positively skewed, the a) ______________ will be in the center, with the b) ______________ to the right and the c) ______________ to the left.

Question 54

Using the formula method, find the median for the following distribution of scores:

Question 55

Use the counting method to determine the median for the following set of scores: 6, 8, 7, 9, 5, 12, 6, 8

Question 56

Use the counting method to determine the median for the following set of scores: 36, 42, 23, 54, 28, 34, 18

Question 57

Given the following distribution table:
a. What is the mode?
b. What is the mean?

Question 58

On the first day of class, a psychology professor gave her abnormal psychology students a 100-point pretest over concepts related to mental illness. The scores were as follows:
a. Construct a grouped frequency distribution.
b. What is the median?
c. What is the mean?