Deck 4: Summarizing Data: Measures of Variation

Question 1

Which of the following is a measure of variation?

A) the mean
B) the median
C) the midquartile
D) the semi-interquartile range

Answer 1

the semi-interquartile range

Question 2

In order to compare the values of two numbers which belong to different sets of data, we use:

A) $z$ -scores.
B) Chebyshev's theorem.
C) the coefficient of variation.
D) the semi-interquartile range.

Answer 2

$z$ -scores.

Question 3

The measure of variation that is most affected by outliers is the:

A) range.
B) interquartile range.
C) standard deviation.
D) variance.

Answer 3

range.

Question 4

The _______ is not a measure of variation.

A) range
B) midrange
C) semi-interquartile range
D) mean deviation

Question 5

A set of data has a mean of 80 and a standard deviation of 5 . To determine two values that contain at least $\frac{8}{9}$ of the data, we use:

A) Chebyshev's theorem.
B) the coefficient of variation.
C) $z$ -scores.
D) the empirical rule.

Question 6

In order to measure the dispersion of a set of data relative to its level of magnitude, we use:

A) $z$ -scores.
B) Chebyshev's theorem.
C) the coefficient of variation.
D) the empirical rule.

Question 7

Which of the following symbols represents a sample value, not a population value?

A) $\mu$
B) $\bar{x}$
C) $\sigma$
D) $N$

Question 8

The degree of symmetry of a distribution is given by:

A) the standard deviation.
B) the interquartile range.
C) $S K$ .
D) $Q_{3}$ .

Question 9

Which of the following does not provide an application of the standard deviation?

A) $z$ -scores.
B) Chebyshev's theorem.
C) the coefficient of variation.
D) the midquartile.

Question 10

The interquartile range is a better measure of variation than:

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

Question 11

The grades obtained on a test by twelve students in a class are listed below.
$66,70,68,75,80,86,64,73,80,94,72,91$
-Find the range of the grades.

Question 12

The grades obtained on a test by twelve students in a class are listed below.
$66,70,68,75,80,86,64,73,80,94,72,91$
-Find the standard deviation of the grades.

Question 13

The grades obtained on a test by twelve students in a class are listed below.
$66,70,68,75,80,86,64,73,80,94,72,91$
-Find the variance of the grades.

Question 14

The frequency distribution of grades on a test for a class of 30 students is given below:

-Find the variance of the grades.

Question 15

The frequency distribution of grades on a test for a class of 30 students is given below:

-Find the standard deviation of the grades.

Question 16

At the start of the program, ten dieters entering a weight-loss program have the weights (in pounds) shown below. $182,160,120,140,155,136,115,190,144,200$

-For this data, find the hinges.

Question 17

At the start of the program, ten dieters entering a weight-loss program have the weights (in pounds) shown below. $182,160,120,140,155,136,115,190,144,200$

-For this data, construct a boxplot.

Question 18

At the start of the program, ten dieters entering a weight-loss program have the weights (in pounds) shown below. $182,160,120,140,155,136,115,190,144,200$

-For this data, using the hinges as quartiles, find the interquartile range.

Question 19

The number of sales of homes having two bedrooms or less in a state for a ten-week period in 1987 is given in the following table:

-For a two-bedroom or less home in this state during the given period, find the variance of the prices.

Question 20

The number of sales of homes having two bedrooms or less in a state for a ten-week period in 1987 is given in the following table:

-For a two-bedroom or less home in this state during the given period, find the standard deviation of the price.

Question 21

Table 2
Two companies have the following sales results for a particular month.


-Use the data in Table 2 to solve the following:
A salesperson with $\$ 6000$ of sales has lower sales relative to the mean in which of the two companies?

Question 22

Table 2
Two companies have the following sales results for a particular month.


-Use the data in Table 2 to solve the following:
In company 1 , at least what percentage of salespersons have sales between $\$ 7000$ and $\$ 9000$ ?

Question 23

Table 2
Two companies have the following sales results for a particular month.


-Use the data in Table 2 to solve the following:
In company 1 , between what values does at least $35 / 36$ of the salespersons' sales fall?

Question 24

Table 2
Two companies have the following sales results for a particular month.


-Use the data in Table 2 to solve the following:
Give the coefficient of variation of the sales of each of the two companies.

Question 25

How does the interquartile range compare to the range when the distribution is shaped like the cross section of a bell?

Question 26

How does the interquartile range compare to the range when the distribution is shaped like a U?

Question 27

The prices (in dollars) of 16 film video cassettes on sale at a video store are given below.
$38,32,38,13,23,38,32,28,27,32,23,27,25,32,27,30$
-For this data, find the range.

Question 28

The prices (in dollars) of 16 film video cassettes on sale at a video store are given below.
$38,32,38,13,23,38,32,28,27,32,23,27,25,32,27,30$
-For this data, find the standard deviation (if the data is viewed as a population).

Question 29

The prices (in dollars) of 16 film video cassettes on sale at a video store are given below.
$38,32,38,13,23,38,32,28,27,32,23,27,25,32,27,30$
-For this data, find the Pearsonian coefficient of skewness.

Question 30

The following is a list of the number of dollars a sample of students say they are willing to spend for a present for a close friend.
Males: $25,80,30,50,45,30,260,60,50$
Females: $15,35,60,55,40,90,100,25,30$
-Find the range for the entire group.

Question 31

The following is a list of the number of dollars a sample of students say they are willing to spend for a present for a close friend.
Males: $25,80,30,50,45,30,260,60,50$
Females: $15,35,60,55,40,90,100,25,30$
-Find the standard deviation for the females.

Question 32

The following is a list of the number of dollars a sample of students say they are willing to spend for a present for a close friend.
Males: $25,80,30,50,45,30,260,60,50$
Females: $15,35,60,55,40,90,100,25,30$
-Find the interquartile range for the males.

Question 33

The mean, median, and standard deviation of a list of numbers are 128, 160, and 8.2. Suppose that the number 25 is added to each number in the list.
-What is the new value of the mean?

Question 34

The mean, median, and standard deviation of a list of numbers are 128, 160, and 8.2. Suppose that the number 25 is added to each number in the list.
-What is the new value of the median?

Question 35

The mean, median, and standard deviation of a list of numbers are 128, 160, and 8.2. Suppose that the number 25 is added to each number in the list.
-What is the new value of the standard deviation?

Question 36

The mean, median, and standard deviation of a list of numbers are 128, 160, and 8.2. Suppose that the number 25 is added to each number in the list.
-What is the new value of the variance?

Question 37

A measure of variation that is greatly affected by extreme values is the standard deviation.

Question 38

Distributions having a tail to the right are called negative skewed.

Question 39

The midrange is a measure of variation.

Question 40

The standard deviation of the numbers $7,7,7, \ldots, 7$ is zero.

Question 41

In a boxplot, if the median is close to the left side of the box, the data is symmetric.

Question 42

An outlier is an extreme value in the data that may be due to an error in measurement.

Question 43

A measure of variation that depends on all the data is a range.

Question 44

The symbol $s$ represents the population standard deviation.

Question 45

If the mean of a set of data is negative, then the standard deviation is negative.

Question 46

If the mean and standard deviation of a set of data are 60 and 5 respectively, then the values 50 and 70 have $z$ -scores which are equal in magnitude, but opposite in sign.

Question 47

One advantage of the computing formula for the standard deviation is that it does not require calculating the _______.

Question 48

The number of standard deviations a value lies above or below the mean is given by a _______.

Question 49

The symbol $\sigma$ denotes the _______.

Question 50

A denominator of $(n-1)$ in the defining formula for a standard deviation indicates that the formula measures the variance of a _______.

Question 51

A disadvantage that the range has compared to the standard deviation is that the range is _______.

Question 52

If a distribution has the general shape of the cross section of a bell, then the _______ allows for a stronger statement than Chebyshev's theorem.

Question 53

In order to compare the variability of several populations having different magnitude levels, we should use the _______.

Question 54

The closer the Pearsonian coefficient of skewness is to _______ the more symmetric the distribution.

Question 55

When drawing a boxplot, we usually omit _______ from the data.

Question 56

The three measures that are needed to calculate the Pearsonian coefficient of skewness are the mean, the median, and the _______.