# Chapter 3

What is the mean for the following sample of scores? Scores: 1, 4, 5, 6

a) 16
b) 8
c) 4.5
d) 4*

A population of n = 8 scores has EX = 40. What is the population mean?

a) 320
b) 20
c) 5*
d) 0.2

What is the mean for the population of scores shown in the frequency distribution table?
X f
5 2
4 1
3 3
2 2
1 2

a) 15/5 = 3
b) 15/10 = 1.50
c) 29/5 = 5.80
d) 29/10 = 2.90*

A sample has a mean of M = 90. If each score in the sample is multiplied by 5, then what is the mean for the new distribution?

a) 18
b) 85
c) 95
d) 450*

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) all 3 of the other choices are correct

The mean is considered to the "balance point" for a distribution because exactly half of the scores are located above the mean and exactly half are below the mean. T or F?

False

Adding a new score to a distribution will always change the value of the mean. T or F?

False

Changing the value of a score in a distribution will always change the value of the mean. T or F?

True

What is the value of the median for the following set of scores? Scores: 1, 3, 4, 6, 8, 12, 13, 23, 25, 26

a) 7
b) 8
c) 10*
d) 12.5

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

What is the median for the population of scores shown in the frequency distribution table?
X f
5 1
4 2
3 3
2 4
1 2

a) 2.5*
b) 3
c) 3.5
d) 4

Which of the following statements cannot be true for a distribution of scores?

a) 60% of the scores are above the mean
b) 60% of the scores are above the median
c) 60% of the scores are above the mode
d) all of the other options are false statements*

For a 100-point exam, a score of X = 65 is definitely above the median. T or F?

False

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

True

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

Which of the following statements cannot be true for a distribution of scores?

a) no one has a score exactly equal to the mean
b) no one has a score exactly to the median
c) no one has a score exactly to the mode*
d) all of the other options are false statements

Which of the following statements is true?

a) it is possible for a distribution to have two means
b) it is possible for a distribution to have two medians
c) it is possible for a distribution to have two modes*
d) it is possible for a distribution to have two medians or two modes

For any distribution of scores, at least one individual will have a score exactly equal to the mean. T or F?

False

It is possible for a distribution to have more than one mode. T or F?

True

It is possible to have a distribution of scores where no individual has a score exactly equal to the mode. T or F?

False

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) any of the three measure could be used

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 t

a) the mean
b) the median*
c) the mode
d) central tendency cannot be determined for these data

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 the

a) the mean
b) the median*
c) the mode
d) central tendency cannot be determined for these data

Under what circumstances is the median likely to produce a better measure of central tendency than the mean?

a) with a symmetrical distribution
b) with an extremely skewed distribution*
c) when the data consist of nominal measurements
d) when the data are numerical scores from an interval or a ratio scale

What is the preferred measure of central tendency for scores measured on an ordinal scale?

a) the mean
b) the median*
c) the mode
d) central tendency cannot be determined for ordinal data

A population of scores has mean of u = 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) cannot be determined from the information given

What is the most likely shape for a distribution with a mean of 40 and a mode of 45?

a) symmetrical
b) positively skewed
c) negatively skewed*
d) either positively or negatively skewed

For a perfectly symmetrical distribution with u = 30, what is the mode?

a) 30
b) greater than 30
c) less than 30
d) cannot be determined from the information given*

A distribution is positively skewed. Which is the most probably 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

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

a) 30*
b) greater than 30
c) less than 30
d) cannot be determined from the information given

For a set of scores measured on an ordinal scale, the median is preferred to the mean as a measure of central tendency. T or F?

True

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

True

For a severely skewed distribution, the median often provides a better measure of central tendency than the mean. T or F?

True

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

True

It is impossible for the value of the mode to be greater than the value of the mean. T or F?

False