Deck 3: Descriptive Statistics: Numerical Measures

Question 1

Which of the following descriptive statistics is not measured in the same units as the data?

A)35^th percentile
B)standard deviation
C)variance
D)interquartile range

Answer 1

C

Question 2

The interquartile range is the difference between the

A)first and second quartiles
B)first and third quartiles
C)second and third quartiles
D)second and fourth quartiles

Answer 2

B

Question 3

The coefficient of variation indicates how large the standard deviation is relative to the

A)mean
B)median
C)range
D)variance

Answer 3

A

Question 4

A numerical measure, such as a mean, computed from a population is known as a

A)population parameter
B)sample parameter
C)sample statistic
D)sample mean

Question 5

After the data has been arranged from smallest value to largest value, the value in the middle is called the

A)range
B)median
C)mean
D)None of the other answers are correct.

Question 6

In computing descriptive statistics for grouped data, the ____ are used to approximate the data values in each class.

A)class lower limits
B)class upper limits
C)class midpoints
D)class ranges

Question 7

The measure of variability easiest to compute, but seldom used as the only measure, is the

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

Question 8

$\mu$ is an example of a

A)population parameter
B)sample statistic
C)population variance
D)mode

Question 9

Which of the following is not a measure of variability of a single variable?

A)range
B)covariance
C)standard deviation
D)coefficient of variation

Question 10

A numerical measure computed from a sample, such as sample mean, is known as a

A)population parameter
B)sample parameter
C)sample statistic
D)population mean

Question 11

An important measure of location for categorical data is the

A)mean
B)median
C)mode
D)margin

Question 12

The mean of the sample

A)is always larger than the mean of the population from which the sample was taken
B)is always smaller than the mean of the population from which the sample was taken
C)can never be zero
D)None of the other answers are correct.

Question 13

The empirical rule states that, for data having a bell-shaped distribution, the percentage of data values being within one standard deviation of the mean is approximately

A)33
B)50
C)68
D)95

Question 14

If a data set has an even number of observations, the median

A)cannot be determined
B)is the average value of the two middle items
C)must be equal to the mean
D)is the average value of the two middle items when all items are arranged in ascending order

Question 15

The mean of a sample is

A)always equal to the mean of the population
B)always smaller than the mean of the population
C)computed by summing the data values and dividing the sum by (n - 1)
D)computed by summing all the data values and dividing the sum by the number of items

Question 16

Since the population size is always larger than the sample size, then the sample statistic

A)can never be larger than the population parameter
B)can never be equal to the population parameter
C)can never be zero
D)None of the other answers are correct.

Question 17

The coefficient of determination is equal to the

A)absolute value of the correlation coefficient
B)squared value of the correlation coefficient
C)square-root of the correlation coefficient
D)inverse value of the correlation coefficient

Question 18

Generally, which one of the following is the least appropriate measure of central tendency for a data set that contains outliers?

A)mean
B)median
C)2^nd quartile
D)50^th percentile

Question 19

Since the population is always larger than the sample, the value of the sample mean

A)is always smaller than the true value of the population mean
B)is always larger than the true value of the population mean
C)is always equal to the true value of the population mean
D)could be larger, equal to, or smaller than the true value of the population mean

Question 20

A box plot is a graphical representation of data that is based on

A)the empirical rule
B)z-scores
C)a histogram
D)a five-number summary

Question 21

In computing the p^th percentile, if the index i is an integer the p^th percentile is the

A)data value in position i
B)data value in position i + 1
C)average of data values in position i and i + 1
D)average of data values in position i - 1 and i + 1

Question 22

Exhibit 3-1
A researcher has collected the following sample data.
The interquartile range is

A)the 50th percentile
B)another name for the variance
C)the difference between the largest and smallest values
D)the difference between the third quartile and the first quartile

Question 23

The first quartile

A)contains at least one third of the data elements
B)is the same as the 25th percentile
C)is the same as the 50th percentile
D)is the same as the 75th percentile

Question 24

Excel provides functions for computing the

A)mean
B)median
C)mode
D)Excel provides functions for all of these.

Question 25

Exhibit 3-1
A researcher has collected the following sample data.
Refer to Exhibit 3-1. The mode is

A)5
B)6
C)7
D)8

Question 26

Exhibit 3-1
A researcher has collected the following sample data.
Refer to Exhibit 3-1. The 75th percentile is

A)6
B)7
C)8
D)9

Question 27

The measure of location that is the most likely to be influenced by extreme values in the data set is the

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

Question 28

Since the mode is the most frequently occurring data value, it

A)can never be larger than the mean
B)is always larger than the median
C)is always larger than the mean
D)None of the other answers are correct.

Question 29

The 75th percentile is also the

A)first quartile
B)second quartile
C)third quartile
D)fourth quartile

Question 30

The most frequently occurring value of a data set is called the

A)range
B)mode
C)mean
D)None of the other answers are correct.

Question 31

The 50th percentile is the

A)mode
B)median
C)mean
D)third quartile

Question 32

The median of a sample will always equal the

A)mode
B)mean
C)50th percentile
D)all of these answers are correct

Question 33

Exhibit 3-1
A researcher has collected the following sample data.
Refer to Exhibit 3-1. The median is

A)5
B)6
C)7
D)8

Question 34

Exhibit 3-1
A researcher has collected the following sample data.
Refer to Exhibit 3-1. The mean is

A)5
B)6
C)7
D)8

Question 35

Excel's __________ function can be used to compute the mode.

A)MAX
B)AVERAGE
C)MEDIAN
D)MODE

Question 36

Excel's __________ function can be used to compute the mean.

A)MAX
B)AVERAGE
C)MEDIAN
D)MODE

Question 37

Which of the following is not a measure of location?

A)mean
B)median
C)variance
D)mode

Question 38

Since the median is the middle value of a data set, it must always be

A)smaller than the mode
B)larger than the mode
C)smaller than the mean
D)None of the other answers are correct.

Question 39

Excel's __________ function can be used to compute the median.

A)MAX
B)AVERAGE
C)MEDIAN
D)MODE

Question 40

Exhibit 3-1
A researcher has collected the following sample data.
The difference between the largest and the smallest data values is the

A)variance
B)interquartile range
C)range
D)coefficient of variation

Question 41

Exhibit 3-1
A researcher has collected the following sample data.
The sample variance

A)is always smaller than the true value of the population variance
B)is always larger than the true value of the population variance
C)could be smaller, equal to, or larger than the true value of the population variance
D)can never be zero

Question 42

The variance of the sample

A)can never be negative
B)can be negative
C)cannot be zero
D)cannot be less than one

Question 43

Exhibit 3-1
A researcher has collected the following sample data.
The interquartile range is used as a measure of variability to overcome what difficulty of the range?

A)the sum of the range variances is zero
B)the range is difficult to compute
C)the range is influenced too much by extreme values
D)the range is negative

Question 44

Excel's __________ function can be used to compute the sample standard deviation.

A)MAX
B)MODE
C)VAR
D)STDEV

Question 45

Which of the following is a measure of dispersion?

A)percentiles
B)quartiles
C)interquartile range
D)all of these are measures of dispersion

Question 46

The sum of deviations of the individual data elements from their mean is

A)always greater than zero
B)always less than zero
C)sometimes greater than and sometimes less than zero, depending on the data elements
D)always equal to zero

Question 47

The coefficient of variation is

A)the same as the variance
B)the square root of the variance
C)the square of the standard deviation
D)None of the other answers are correct.

Question 48

Which of the following is not a measure of dispersion?

A)the range
B)the 50th percentile
C)the standard deviation
D)the interquartile range

Question 49

If the variance of a data set is correctly computed with the formula using n - 1 in the denominator, which of the following is true?

A)the data set is a sample
B)the data set is a population
C)the data set could be either a sample or a population
D)the data set is from a census

Question 50

The numerical value of the standard deviation can never be

A)larger than the variance
B)zero
C)negative
D)all of these statements are correct

Question 51

During a cold winter, the temperature stayed below zero for ten days (ranging from -20 to -5). The variance of the temperatures of the ten day period

A)is negative since all the numbers are negative
B)must be at least zero
C)cannot be computed since all the numbers are negative
D)can be either negative or positive

Question 52

The value of the sum of the squared deviations from the mean, i.e., must always be

A)less than the mean
B)negative
C)either positive or negative depending on whether the mean is negative or positive
D)at least zero

Question 53

The variance of a sample of 81 observations equals 64. The standard deviation of the sample equals

A)0
B)4096
C)8
D)6,561

Question 54

Excel's __________ function can be used to compute the population standard deviation.

A)MAX
B)MODE
C)STDEV
D)None of the other answers are correct.

Question 55

Excel's __________ function can be used to compute the population variance.

A)MAX
B)MODE
C)VAR
D)None of the other answers are correct.

Question 56

The population variance can never be

A)zero
B)larger than the standard deviation
C)negative
D)all of these are correct

Question 57

The standard deviation of a sample of 100 observations equals 64. The variance of the sample equals

A)8
B)10
C)6,400
D)4,096

Question 58

The measure of dispersion that is influenced most by extreme values is

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

Question 59

The weights (in pounds) of a sample of 36 individuals were recorded and the following statistics were calculated The coefficient of variation equals

A)0.1125%
B)11.25%
C)203.12%
D)0.20312%

Question 60

Excel's __________ function can be used to compute the sample variance.

A)MAX
B)MODE
C)VAR
D)STDEV

Question 61

Exhibit 3-2
A researcher has collected the following sample data. The mean of the sample is 5.
Refer to Exhibit 3-2. The variance is

A)80
B)4.062
C)13.2
D)16.5

Question 62

Which of the following symbols represents the variance of the population?

A) $\sigma$ ²
B) $\sigma$
C) $\mu$
D)n

Question 63

Which of the following symbols represents the mean of the population?

A) $\sigma$ ²
B) $\sigma$
C) $\mu$
D)n

Question 64

Exhibit 3-2
A researcher has collected the following sample data. The mean of the sample is 5.
Refer to Exhibit 3-2. The coefficient of variation is

A)72.66%
B)81.24%
C)264%
D)330%

Question 65

The descriptive measure that is not measured in the same units as the original data is the

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

Question 66

The descriptive measure of dispersion that is based on the concept of a deviation about the mean is

A)the range
B)the interquartile range
C)both the range and the interquartile range
D)the standard deviation

Question 67

Exhibit 3-2
A researcher has collected the following sample data. The mean of the sample is 5.
Refer to Exhibit 3-2. The interquartile range is

A)1
B)2
C)10
D)12

Question 68

The symbol $\sigma$ is used to represent the

A)variance of the population
B)standard deviation of the sample
C)standard deviation of the population
D)None of the other answers are correct.

Question 69

Which of the following symbols represents the size of the sample?

A) $\sigma$ ²
B) $\sigma$
C)N
D)n

Question 70

Exhibit 3-2
A researcher has collected the following sample data. The mean of the sample is 5.
The __________ denotes the number of standard deviations x_i is from the mean .

A)range
B)median
C)z-score
D)third quartile

Question 71

Exhibit 3-2
A researcher has collected the following sample data. The mean of the sample is 5.
Refer to Exhibit 3-2. The range is

A)1
B)2
C)10
D)12

Question 72

Exhibit 3-2
A researcher has collected the following sample data. The mean of the sample is 5.
__________ can be used to make statements about the proportion of data values that must be within a specified number of standard deviations of the mean.

A)Chebyshev's theorem
B)The empirical rule
C)A five-number summary
D)A box plot

Question 73

Which of the following symbols represents the mean of the sample?

A) $\sigma$ ²
B) $\sigma$
C) $\mu$
D)n

Question 74

Exhibit 3-2
A researcher has collected the following sample data. The mean of the sample is 5.
__________ can be used to determine the percentage of data values that must be within one, two, and three standard deviations of the mean for data having a bell-shaped distribution.

A)Chebyshev's theorem
B)empirical rule
C)five-number summary
D)box plot

Question 75

If two groups of numbers have the same mean, then their

A)standard deviations must also be equal
B)medians must also be equal
C)modes must also be equal
D)None of the other answers are correct.

Question 76

Exhibit 3-2
A researcher has collected the following sample data. The mean of the sample is 5.
Refer to Exhibit 3-2. The standard deviation is

A)8.944
B)4.062
C)13.2
D)16.5

Question 77

Exhibit 3-2
A researcher has collected the following sample data. The mean of the sample is 5.
A(n) __________ is an unusually small or unusually large data value.

A)sample statistic
B)median
C)z-score
D)outlier

Question 78

Which of the following symbols represents the size of the population?

A) $\sigma$ ²
B) $\sigma$
C) $\mu$
D)N

Question 79

Which of the following symbols represents the standard deviation of the population?

A) $\sigma$ ²
B) $\sigma$
C) $\mu$
D)None of the other answers are correct.

Question 80

The symbol $\sigma$ ² is used to represent the

A)variance of the population
B)standard deviation of the sample
C)standard deviation of the population
D)None of the other answers are correct.