Deck 4: Measures of Variation

Question 1

Four students have applied to a special program and only one can be accepted. They have taken a battery of 12 tests and all have exactly the same average score. The standard deviation of their test scores are: Student A = 3.12, Student B = 0.27, Student C = 13.45, Student D = 6.45. If consistency of performance is a criterion for acceptance, which of the four students should be selected?

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

Answer 1

B

Question 2

The expression instructs us to ________.

A) square the sum of the scores.
B) sum the squared scores.
C) sum the squared deviations.
D) square the summed deviations.

Answer 2

C

Question 3

As a distribution of scores becomes more variable, the value of the standard deviation________.

A) decreases.
B) stays the same.
C) increases.
D) becomes unpredictable.

Answer 3

increases.

Question 4

If distribution A and distribution B have the same mean but A has a larger standard deviation, we may conclude that________.

A) the medians of both distributions would be the same.
B) distribution B has a range of 0.
C) A has a greater degree of variation.
D) distribution B displays more variety.

Question 5

Which measure of variation is most important and most commonly used in social science research?

A) The range
B) The average deviation
C) The median
D) The standard deviation

Question 6

The expression instructs us to _______.

A) sum the scores.
B) sum the scores and then subtract the mean.
C) subtract every "ith" score from the mean.
D) subtract the mean from each score and add up the deviations.

Question 7

The greater the skew of a distribution of scores, ________.

A) the lower the value of the standard deviation.
B) the higher the value of the standard deviation.
C) the lower the value of the range.
D) None of the answer choices: measures of variation are not affected by skew.

Question 8

According to the data presented in the text, incomes in the US are________.

A) falling for the average family.
B) rising for everyone except the very rich.
C) decreasing in variation (income inequality is decreasing).
D) increasing in variation (income inequality is increasing).

Question 9

Measures of variation provide information about the________.

A) typical or most common score.
B) variety within the distribution of scores.
C) size of the sample.
D) adequacy of the selection criteria for the sample.

Question 10

The lower limit for the standard deviation is 0; the upper limit is________.

A) the score of the mean.
B) the score of the median.
C) a function of the number of cases.
D) undefined; there is no upper limit.

Question 11

If a variable is interval-ratio in level of measurement, the preferred measure of variation would be________.

A) the mean.
B) the range.
C) the standard deviation.
D) the percentile.

Question 12

Which of the following is a correct description of the distribution of income in the US since the 1960s?

A) The mean income has risen but the median has fallen.
B) Both the mean and the median have risen but the mean has increased more.
C) There is a noticeable negative skew in the distribution.
D) The distribution has grown less variable.

Question 13

When you subtract the value of the mean from each score in a distribution and then add the results, the sum will be________.

A) 0.
B) the standard deviation.
C) the variance.
D) a positive number.

Question 14

If the standard deviation of a group of scores is 0,________.

A) the range would be at a maximum value.
B) there is maximum variation in the scores.
C) there is no variation in the scores.
D) the mean is larger than the median.

Question 15

If the variance of a distribution is 16, the mean is 12, and the number of cases is 24, the standard deviation is________.

A) 4.
B) 6.
C) 8.
D) 12.

Question 16

Measures of central tendency (like the mean) and measures of variation (like the range) provide information about distributions of scores which is________.

A) contradictory.
B) redundant.
C) unnecessary.
D) complementary.

Question 17

The standard deviation(s)________.

A) squares the deviations to eliminate negative values.
B) decreases in value as distributions become more heterogeneous.
C) does not use all the scores.
D) is based on the median rather than the mean.

Question 18

The age of a sample has been measured in years. Which of the following would be the preferred measure of the variation for this variable?

A) The index of qualitative variation
B) The average deviation
C) The quartile deviation
D) The standard deviation

Question 19

The information below compares the final exam grades for 2 biology classes: What may we conclude? Class 1 _______.

A) is more homogeneous.
B) is more heterogeneous.
C) was a better class.
D) had no grade higher than a 90.

Question 20

The income of a sample has been measured in dollars per year. Which of the following would be the preferred measure of the variation for this variable?

A) The index of qualitative variation
B) The average deviation
C) The quartile deviation
D) The standard deviation

Question 21

In a boxplot, an outlier is defined as a score that is________.

A) greater than 1.5 times the height of the box.
B) less than 1.5 times the height of the box.
C) greater than 1.25 times the height of the box.
D) greater than 0.75 times the height of the box.

Question 22

The distances between the scores and the mean are called________.

A) deviations.
B) differences.
C) ranges.
D) summations.

Question 23

The interquartile range would be an appropriate measure of variation for________.

A) nominal level variables.
B) continuous interval-ratio level variables only.
C) ordinal level variables.
D) discrete interval-ratio level variables only.

Question 24

The second quartile (Q2) is equal in value to________.

A) the mode.
B) the median.
C) the mean.
D) the range.

Question 25

A boxplot uses what to show the range of scores?

A) slices
B) bars
C) points
D) whiskers

Question 26

A boxplot uses all but which of the following to present dispersion?

A) median
B) third quartile (Q 3 )
C) standard deviation
D) first quartile (Q 1 )

Question 27

When measures of central tendency and dispersion are presented in the literature, the number of cases may vary from variable to variable. This is because________.

A) the researchers only used a subset of their sample for convenience purposes.
B) cases were missing values for that variable.
C) the variable in those cases was measured at a different level.
D) none of these choices are correct.

Question 28

If a distribution of scores has a mean of 30 and a range of 0________.

A) the variance is 30.
B) the quartile deviation (Q) is 10.
C) there is no variation in the distribution.
D) the standard deviation is 1.

Question 29

A graph used to visualize and analyze variation is a________.

A) pie chart.
B) boxplot.
C) histogram.
D) line chart.

Question 30

Your score on the test is the same as the third quartile (Q3). You may conclude that________.

A) you scored higher than 75% of the people who took the test.
B) the distribution of the scores is skewed.
C) your score is 'typical' since it is the same value as the median.
D) you scored higher than 25% of the people who took the test.

Question 31

Which of the following data sets shows the greatest variability?

A) 9, 10, 11
B) 0, 5, 9
C) 50, 60, 170
D) 31, 33, 35

Question 32

Since the 1960s, the income associated with the 80th percentile has ________ and the income associated with the 20th percentile has ________.

A) risen, risen
B) stayed roughly the same, risen
C) fallen, risen
D) risen, stayed roughly the same

Question 33

The scores below are from the same final exam given in a math class in two different years. Compute the mean and median (if necessary) and the range and standard deviation of these scores. Using these statistics, describe the differences in the two sets of scores.

Question 34

Measures of variation indicate the degree to which a set of scores is________.

A) heterogeneous.
B) ambiguous.
C) average.
D) typical.

Question 35

Boxplots depict________.

A) central tendency.
B) dispersion.
C) both central tendency and dispersion.
D) None of these choices are correct.

Question 36

Some information about auto theft rates (number of auto thefts per 100,000 population) for a sample of 178 cities in two different years is summarized below.
Express this statistical information in words. What changes were there in the overall shape of the variation of this variable? In central tendency? In dispersion?

Question 37

The range (R) is found by subtracting the lowest from the highest score in the distribution. Therefore, R could NOT be found for________.

A) nominal level variables.
B) discrete variables.
C) ordinal level variables.
D) continuous variables.