Deck 3: Descriptive Statistics: Numerical Measures

Question 1

The median of a sample will always equal the

A) (Q1 + Q3)/2.
B) square root of the variance.
C) 50th percentile.
D) (smallest value + largest value)/2.

Answer 1

50th percentile.

Question 2

The median is a measure of

A) relative dispersion.
B) absolute dispersion.
C) central location.
D) relative location.

Answer 2

central location.

Question 3

Which of the following provides a measure of central tendency for the data?

A) Standard deviation
B) Mean
C) Variance
D) Range

Answer 3

Mean

Question 4

Geometric mean is a measure of

A) location.
B) dispersion.
C) variability.
D) weight.

Question 5

When a percentage of the smallest and largest values are deleted from a data set, the mean of the remaining data values is the _____ mean.

A) geometric
B) weighted
C) trimmed
D) interquartile

Question 6

The 75th percentile is referred to as the _____ quartile.

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

Question 7

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 8

A numerical value used as a summary measure for a sample is known as a sample

A) error.
B) parameter.
C) statistic.
D) value.

Question 9

The 50th percentile is the

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

Question 10

If two groups of numbers have the same mean, then

A) their standard deviations must also be equal.
B) their medians must also be equal.
C) their modes must also be equal.
D) other measures of location need not be the same.

Question 11

In computing the mean of a sample, the value of ∑x_i is divided by

A) n.
B) n - 1.
C) n + 1.
D) n - 2.

Question 12

Growth factors for the population of Chattanooga in the past two years have been 8 and 12. The geometric mean has a value of

A) 20.
B) .
C) .
D) 96.

Question 13

μ is an example of a

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

Question 14

The geometric mean of four observations is the

A) same as their weighted mean.
B) same as their arithmetic mean.
C) square root of the product of the 4 observations.
D) fourth root of the product of the 4 observations.

Question 15

The nth root of the product of the n observations is the

A) weighted mean.
B) geometric mean.
C) product deviation.
D) product variance.

Question 16

The mean of the sample

A) is always smaller than the mean of the population from which the sample was taken.
B) can never be zero.
C) can never be negative.
D) can assume any value between the highest and the lowest value in the sample.

Question 17

Growth factors for the population of Atlanta in the past five years have been 1, 2, 3, 4 , and 5. The geometric mean is

A) 15.
B) .
C) .
D) .

Question 18

The variance of a sample of 144 observations equals 576. The standard deviation of the sample equals

A) 12.
B) 21.
C) 441.
D) 63,504.

Question 19

The measure of location which 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 20

​The hourly wages of a sample of 130 system analysts are given below. ​ ​
The coefficient of variation equals
​

A) ​0.30%.
B) ​30%.
C) ​5.4%.
D) ​54%.

Question 21

When data are positively skewed, the mean will usually be

A) greater than the median.
B) smaller than the median.
C) equal to the median.
D) positive.

Question 22

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

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

Question 23

The pth percentile is a value such that approximately

A) p percent of the observations are less than the value and (100 - p) percent are more than this value.
B) p percent of the observations are less than the value and p percent are more than this value.
C) (100 - p) percent of the observations are less than the value and p percent are more than this value.
D) (100 - p) percent of the observations are less than the value and (100 - p) percent are more than this value.

Question 24

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

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

Question 25

Which difficulty of range as a measure of variability is overcome by interquartile 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 26

Which of the following is not a measure of central location?

A) Mean
B) Median
C) Standard deviation
D) Mode

Question 27

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

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

Question 28

The value which has half of the observations above it and half the observations below it is called the

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

Question 29

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 30

The interquartile range is

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

Question 31

Which of the following is not a measure of variability?

A) The range
B) The midrange
C) The standard deviation
D) The interquartile range

Question 32

When n - 1 is used in the denominator to compute variance, the data set

A) is a sample.
B) is a population.
C) could be either a sample or a population.
D) is from a census.

Question 33

When computing the mean, the smallest value

A) can never be negative.
B) can never be zero.
C) can never be less than the mean.
D) can be any value.

Question 34

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

A) 8.
B) 10.
C) 4096.
D) 10,000.

Question 35

When the data are skewed to the right, the measure of Skewness will be

A) negative.
B) zero.
C) positive.
D) one.

Question 36

The first quartile is the same as the

A) median.
B) 25th percentile.
C) 50th percentile.
D) 75th percentile.

Question 37

Which of the following is a measure of variability?

A) Percentiles
B) Quartiles
C) Interquartile range
D) Midrange

Question 38

In computing descriptive statistics from grouped data,

A) data values are treated as if they occur at the midpoint of a class.
B) the grouped data result is more accurate than the ungrouped result.
C) the grouped data computations are used only when a population is being analyzed.
D) none of these alternatives is correct.

Question 39

The standard deviation of a sample of 81 observations equals 49. The variance of the sample equals

A) 7.
B) 9.
C) 2401.
D) 6561.

Question 40

The heights (in inches) of 25 individuals were recorded and the following statistics were calculated mean = 70
Range = 20
Mode = 73
Variance = 784
Median = 74
The coefficient of variation equals

A) 11.2%.
B) 1120%.
C) 0.4%.
D) 40%.

Question 41

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

A) σ²
B) σ
C) μ
D)

Question 42

A numerical measure of linear association between two variables is the

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

Question 43

The symbol σ is used to represent the

A) variance of the population.
B) standard deviation of the sample.
C) standard deviation of the population.
D) variance of the sample.

Question 44

The variance can never be

A) the same as the standard deviation.
B) larger than the standard deviation.
C) negative.
D) smaller than the standard deviation.

Question 45

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

A) σ²
B) σ
C) μ
D)

Question 46

The numerical value of the standard deviation can never be

A) larger than the variance.
B) zero.
C) negative.
D) smaller than the variance.

Question 47

The symbol σ² is used to represent the

A) variance of the population.
B) standard deviation of the sample.
C) standard deviation of the population.
D) variance of the sample.

Question 48

The coefficient of variation is the

A) same as the variance.
B) standard deviation divided by the mean times 100.
C) square of the standard deviation.
D) mean divided by the standard deviation.

Question 49

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 50

The descriptive measure of variability that is based on the concept of a variation about the mean is the

A) range.
B) interquartile range.
C) absolute value of the range.
D) standard deviation.

Question 51

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 52

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

A) σ²
B) σ
C) μ
D)

Question 53

The measure of dispersion which is not measured in the same units as the original data is the

A) median.
B) standard deviation.
C) coefficient of determination.
D) variance.

Question 54

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

A) σ²
B) σ
C) N
D) n

Question 55

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

A) σ²
B) σ
C) μ
D)

Question 56

The measure of variability that is influenced most by extreme values is the

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

Question 57

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) positive relation between the independent and the dependent variables.

Question 58

The variance of the sample

A) cannot be negative.
B) cannot be positive.
C) cannot be zero.
D) cannot be less than one.

Question 59

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

A) σ²
B) σ
C) μ
D) N

Question 60

When should measures of location and dispersion be computed from grouped data rather than from individual data values?

A) As much as possible since computations are easier
B) Only when individual data values are unavailable
C) Whenever computer packages for descriptive statistics are unavailable
D) Only when the data are from a population

Question 61

Given the following information:​ Standard deviation = 8
Coefficient of variation = 64%
The mean would then be

A) 12.5.
B) 8.
C) 0.64.
D) 1.25.

Question 62

The correlation coefficient ranges between

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

Question 63

From a population of size 500, a random sample of 50 items is selected. The mode of the sample

A) must be 500.
B) must be equal to the mode of population, if the sample is truly random.
C) must be equal to the mean of the population, if the sample is truly random.
D) can be larger, smaller or equal to the mode of the population.

Question 64

The geometric mean of 3, 4, 6 is

A) 2.35.
B) 3.61.
C) 4.16.
D) 8.48.

Question 65

The standard deviation of a sample was reported to be 20. The report indicated that = 7200. What is the sample size?

A) 16
B) 17
C) 18
D) 19

Question 66

If the coefficient of variation is 40% and the mean is 70, then the variance is

A) 28.
B) 2800.
C) 1.75.
D) 784.

Question 67

From a population of size 400, a random sample of 40 items is selected. The median of the sample

A) must be 200, since 400 divided by 2 is 200.
B) must be 10, since 400 divided by 40 is 10.
C) must be equal to the median of population, if the sample is truly random.
D) none of these alternatives is correct.

Question 68

A group of students had dinner at a local restaurant. The total bill for the dinner was $364.99. Each student paid his/her equal share of the bill, which was $21.47. How many student's were at the dinner?

A) 124
B) 365
C) 17
D) 22

Question 69

The coefficient of correlation

A) is the same as the coefficient of determination.
B) cannot be larger than 100.
C) cannot be larger than 1.
D) cannot be negative.

Question 70

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 these alternatives is correct.

Question 71

The geometric mean of 1, 1, 8 is

A) 10.0.
B) 2.0.
C) 3.33.
D) 3.16.

Question 72

The numerical value of the variance

A) is always larger than the numerical value of the standard deviation.
B) is always smaller than the numerical value of the standard deviation.
C) is negative if the mean is negative.
D) can be larger or smaller than the numerical value of the standard deviation.

Question 73

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 74

The relative frequency of a class is computed by dividing the

A) midpoint of the class by the sample size.
B) frequency of the class by the midpoint.
C) sample size by the frequency of the class.
D) frequency of the class by the sample size.

Question 75

​From a population of size 1,000, a random sample of 100 items is selected. The mean of the sample

A) ​must be 10 times smaller than the mean of the population.
B) ​must be equal to the mean of the population, if the sample is truly random.
C) ​must be 10 times larger than the mean of the population.
D) ​can be larger, smaller or equal to the mean of the population.

Question 76

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

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

Question 77

Which of the following is not a measure of variability?

A) Midrange
B) Standard deviation
C) Range
D) Interquartile range

Question 78

The variance of a sample was reported to be 144. The report indicated that = 7200. What is the sample size?

A) 49
B) 50
C) 51
D) 52

Question 79

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

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

Question 80

Since the median is the middle value of a data set it

A) must always be smaller than the mode.
B) must always be larger than the mode.
C) must always be smaller than the mean.
D) none of these alternatives is correct.