Deck 3: Descriptive Statistics: Numerical Measures

Question 1

An important measure of location for categorical data is the _____.

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

Answer 1

mode

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

first and third quartiles

Question 3

Which of the following depicts a moderately left-skewed distribution?

A)
B)
C)
D)

Answer 3

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) population statistic

Question 5

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 6

The variance is equal to the _____.

A) absolute value of the standard deviation
B) squared value of the standard deviation
C) square root of the standard deviation
D) inverse value of the standard deviation

Question 7

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

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

Question 8

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 9

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 statistic

Question 10

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

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

Question 11

After the data have 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 answers is correct.

Question 12

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 13

The empirical rule states that, for data having a bell-shaped distribution, the portion 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 observation recorded most often
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

A graph with skewness -1.8 would be which of the following?

A) moderately skewed left
B) highly skewed left
C) moderately skewed right
D) highly skewed right

Question 16

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 17

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 answers is correct.

Question 18

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 19

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

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

Question 20

In statistics, what does IQR mean?

A) individual quantity range
B) inter-quantity relativity
C) individual quartile relativity
D) inter-quartile range

Question 21

The median of a sample will always equal the _____.

A) mode
B) mean
C) 50th percentile
D) All of the answers are correct.

Question 22

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

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

Question 23

The 50th percentile is the _____.

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

Question 24

The symbol for _____ is r.

A) sample covariance
B) population covariance
C) sample correlation
D) population correlation

Question 25

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

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

Question 26

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 27

The variance of a sample or a population cannot be _____.

A) negative
B) calculated
C) zero
D) less than1

Question 28

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

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

Question 29

Which of the following is NOT a measure of location?

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

Question 30

The difference between the largest and smallest data values is the _____.

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

Question 31

The five-number summary consists of what five statistical measures?

A) min, Q₁, median, Q₃, max
B) Q₁, Q₂, median, Q₃, Q₄
C) min, Q₁, mean, Q₃, max
D) Q₁, Q₂, mean, Q₃, Q₄

Question 32

In computing the pth percentile, if the index i is an integer the pth percentile is the _____.

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

Question 33

The 75th percentile is also the _____.

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

Question 34

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 35

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 and first quartiles

Question 36

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 answers is correct.

Question 37

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 38

Excel's _____ function can be used to compute the middle value of an ordered data set.

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

Question 39

Excel's _____ function can be used to compute the data value occurring most frequently.

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

Question 40

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 answers is correct.

Question 41

The measure of dispersion that is influenced most by extreme values is the _____.

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

Question 42

The symbol for _____ is $\rho$ .

A) sample covariance
B) population covariance
C) sample correlation
D) population correlation

Question 43

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 44

The value of the sum of the squared deviations from the mean, i.e., $\Sigma ( x - \bar { x } ) ^ { 2 }$ 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 45

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 46

The variance of a sample of 81 observations is 64. The standard deviation of the sample is which of the following?

A) 9
B) 4,096
C) 8
D) 6,561

Question 47

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

A) σ ²
B) σ
C) μ
D) N

Question 48

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

A) STDEV.S
B) VAR.SQRT
C) STDEV
D) None of the answers is correct.

Question 49

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

A) VAR.S
B) VAR.C
C) VAR
D) None of the answers is correct.

Question 50

The weight (in pounds) of a sample of 36 individuals was recorded, and the following statistics were calculated. mean = 160
Range = 60
Mode = 165
Variance = 324
Median = 170
The coefficient of variation is _____.

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

Question 51

The standard deviation of a sample of 100 observations is 64. The variance of the sample is which of the following?

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

Question 52

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

A) STDEV
B) VAR.SQRT
C) STDEv
D) STDEV.S

Question 53

The descriptive measure NOT measured in the same units as the original data is the _____.

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

Question 54

During a cold winter, the temperature stayed below zero for 10 days (ranging from -20 to -5). The variance of the temperatures of the 10 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 55

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) neither the range nor the interquartile range

Question 56

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

A) VAR
B) VAR.C
C) VAR.S
D) STDEV.SQ

Question 57

The numerical value of the standard deviation can never be _____.

A) larger than the variance
B) zero
C) negative
D) All of the answers are correct.

Question 58

Which of the following is not a measure of dispersion?

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

Question 59

Which of the following is a measure of dispersion?

A) percentiles
B) quartiles
C) interquartile range
D) All of the answers are correct.

Question 60

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 answers is correct.

Question 61

A numerical measure of linear association between two variables is the _____.

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

Question 62

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

A) ? ²
B) ?
C) ?
D) $\bar { x }$

Question 63

_____ 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) The empirical rule
C) A five-number summary
D) A box plot

Question 64

Positive values of covariance indicate _____.

A) a positive variance of the x values
B) a positive variance of the y values
C) the standard deviation is positive
D) a positive relation between the x and y variables

Question 65

A graphical summary of data that is based on a five-number summary is a _____.

A) histogram
B) stem-and-leaf display
C) scatter diagram
D) box plot

Question 66

_____ 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, regardless of the shape of the distribution.

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

Question 67

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

A) ? ²
B) ?
C) ?
D) $\bar { x }$

Question 68

A numerical measure of linear association between two variables is the _____.

A) variance
B) z-score
C) correlation coefficient
D) None of the answers is correct.

Question 69

The symbol σ is used to represent the _____.

A) variance of a population
B) standard deviation of a sample
C) standard deviation of a population
D) variance of a sample

Question 70

A(n) _____ is an unusually small or unusually large data value.

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

Question 71

The _____ denotes the number of standard deviations x_i is from the mean $\bar { x }$ .

A) variance
B) median
C) z-score
D) normal deviation

Question 72

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

A) σ ²
B) σ
C) N
D) n

Question 73

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

A) ? ²
B) ?
C) ?
D) $\bar { x }$

Question 74

The correlation coefficient ranges from which two values?

A) 0 and 1
B) −1 and +1
C) minus infinity and plus infinity
D) 1 and 100

Question 75

The symbol σ ² is used to represent the _____.

A) variance of a population
B) standard deviation of a sample
C) standard deviation of a population
D) variance of a sample

Question 76

Excel's _____ function can be used to compute the sample covariance.

A) COVARIANCE
B) COVARIANCE.S
C) COVAR
D) COVAR.S

Question 77

In a five-number summary, which of the following is NOT used for data summarization?

A) smallest value
B) largest value
C) median
D) mean

Question 78

The correlation coefficient _____.

A) is the same as the covariance
B) can be larger than 1
C) cannot be larger than 1
D) cannot be negative

Question 79

Excel's _____ function can be used to compute the sample correlation coefficient.

A) CORR.S
B) CORR
C) CORREL.S
D) CORREL

Question 80

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

A) ? ²
B) ?
C) ?
D) $\bar { x }$