Deck 5: Numerical Descriptive Measures

Question 1

A sample of 16 observations has a standard deviation of 2. Which of the following is the sum of the squared deviations from the sample mean?

Answer 1

A

Question 2

What measure of central location is best used with a categorical variable?

Answer 2

D

Question 3

Which of the following is the best measure of variability if the distribution of a set of data is skewed?

Answer 3

D

Question 4

Which of the following statements is true? $\begin{array}{|l|l|}\hline A&\text { The population mean is al ways greater than the sample mean.}\\\hline B&\text {The population mean is always smaller than the sample mean. }\\\hline C&\text {The population mean must always equal the sample mean. }\\\hline D&\text {The population mean may equal, be less than or greater than the population mean. }\\\hline \end{array}$

Question 5

Which of the following statements is true for the following data values: 7, 5, 6, 4, 7, 8 and 12? $\begin{array}{|l|l|}\hline A&\text {The mean, median and mode are all equal. }\\\hline B&\text { Only the mean and median are equal.}\\\hline C&\text {Only the mean and mode are equal. }\\\hline D&\text {Only the median and mode are equal. }\\\hline \end{array}$

Question 6

The average score for a class of 30 students was 75. The 20 male students in the class averaged 70. The female students in the class averaged:

Question 7

Which of the following statements is true? $\begin{array}{|l|l|}\hline A&\text { The standard deviation is always greater than the variance.}\\\hline B&\text {The sum of the squared deviations from the mean is always zero. }\\\hline C&\text { The standard deviation is in squared units.}\\\hline D&\text {The sum of the deviations from each value in a data set to the mean, is always zero. }\\\hline \end{array}$

Question 8

Which of the following summary measures cannot be easily approximated from a box-and-whisker plot?

Question 9

Which of the following best describes the width of the box in the box-and-whisker plot?

Question 10

Which of the following is not a measure of variability?

Question 11

Which of the following statements best describes the mean of a data set?

Question 12

Which of the following statements describes when the median is a better measure of centre than the mean?

Question 13

Which of the following summary measures is affected by extreme values?

Question 14

According to Chebyshev's theorem, which of the following is the percentage of measurements in a data set that fall within three standard deviations of their mean?

Question 15

Which of the following statements is true? $\begin{array}{|l|l|}\hline A&\text { When the distribution is skewed to the left, mean \( > \) median \( > \) mode.}\\\hline B&\text {When the distribution is skewed to the right, mean \( < \) median \( < \) mode. }\\\hline C&\text {When the distribution is symmetric and unimodal, mean \( = \) median \( = \) mode. }\\\hline D&\text { When the distribution is symmetric and bimodal, mean \( = \) median \( = \) mode.}\\\hline \end{array}$

Question 16

Which measure of variability is appropriate when a sample is likely to contain one or several extreme values?

Question 17

According to the empirical rule, which of the following is the approximate percentage of measurements in a data set (provided that the data set has a bell-shaped distribution) that fall within two standard deviations of their mean?

Question 18

Using percentiles, the difference between which of the following is the interquartile range?

Question 19

Which of the following is the proportion of the total area that must be to the left of the median, in a histogram?

Question 20

Which of the following best describes the scenario when two data sets have the same range?

Question 21

When a distribution is symmetric, the mean, median and the mode are all equal.

Question 22

The coefficient of variation allows us to compare two sets of data based on different measurement units.

Question 23

Lily has been keeping track of what she spends on eating out. The last week's expenditures for meals eaten out were $5.69, $5.95, $6.19, $10.91, $7.49, $14.53 and $7.66. The mean amount Lily spends on meals is $8.35.

Question 24

The range is considered the weakest measure of variability.

Question 25

A data sample has a mean of 107, a median of 122 and a mode of 134. The distribution of the data is positively skewed.

Question 26

In a negatively skewed distribution, the mean is smaller than the median and the median is smaller than the mode.

Question 27

In a negatively skewed distribution, the mean is greater than the median.

Question 28

Quartiles divide the values in a data set into four parts of equal size.

Question 29

Which of the following are measures of the linear relationship between two variables?

Question 30

The difference between the largest and smallest values in an ordered array is called the range.

Question 31

In a bell-shaped distribution, there is no difference in the values of the mean, median and mode.

Question 32

A student scores 87, 73, 92 and 86 on four exams during the semester, and 95 on the final exam. If the final is weighted double and the four others weighted equally, the student's final average would be 88.

Question 33

Which of the following statements is true? $\begin{array}{|l|l|}\hline A&\text { The correlation coefficient is -1 if there is a perfect positive correlation between two variables.}\\\hline B&\text { The correlation coefficient is 0 if there is a perfect positive correl ation between two variables.}\\\hline C&\text { The correlation coefficient is 0.5 if there is a perfect positive correlation between two variables.}\\\hline D&\text { The correlation coefficient is 1 if there is a perfect positive correlation between two variables.}\\\hline \end{array}$

Question 34

In a symmetric distribution, the mean is the most used measure of central location for quantitative data.

Question 35

Which of the following must is necessary when approximating descriptive measures for grouped data?

Question 36

Which of the following would be the value of the correlation coefficient of two variables which are not linearly related.

Question 37

The mode is the only measure of central location for a distribution of a nominal (categorical) variable.

Question 38

Which of the following statements is true? $\begin{array}{|l|l|}\hline A&\text {When approximating the sample mean for grouped data we assume that the midpoint of each }\\&\text {class closely approximates the mean of observations in the class. }\\\hline B&\text { When approximating the sample mean for grouped data we cannot assume that the midpoin}\\&\text { of each class closely approximates the mean of observations in the class.}\\\hline C&\text { Descriptive measures for grouped data are not possible.}\\\hline D&\text { None of these choices are correct.}\\\hline \end{array}$

Question 39

Which of the following may be answered by knowing the shape of the distribution? $\begin{array}{|l|l|}\hline A&\text {What is the best measure of central location to use. }\\\hline B&\text {What is the best measure of variability to use. }\\\hline C&\text { What the best measure of central location and variability to use.}\\\hline D&\text { None of these choices are correct.}\\\hline \end{array}$

Question 40

In a positively skewed distribution, the mean is larger than the median and the median is larger than the mode.

Question 41

Chebyshev's theorem states that the percentage of observations in a data set that should fall within 3 standard deviations of their mean is at least 88.9%.

Question 42

When the distribution is skewed, the interquartile range is a better measure of variability than the standard deviation.

Question 43

A courier company is reviewing their delivery times. The following descriptive statistics relates to this courier company. The mean time for package delivery is 5 hours, the first quartile is 4 hours, the third quartile is 17 hours. This means that 75% of deliveries take more than 4 hours?

Question 44

Chebyshev's theorem applies only to data sets that have a mound-shaped distribution.

Question 45

The mean of fifty sales receipts is $65.75 and the standard deviation is $10.55. Using Chebyshev's theorem, at least 75% of the sales receipts were between $44.65 and $86.85.

Question 46

Chebyshev's theorem relates to only to symmetric histograms.

Question 47

A courier company is reviewing their delivery times. The following descriptive statistics relates to this courier company. The mean time for package delivery is 5 hours, the first quartile is 4 hours, the third quartile is 17 hours. This means that the 25% of the deliveries take more than 17 hours.

Question 48

The value of the standard deviation may be either positive or negative, while the value of the variance will always be positive.

Question 49

The boxplot may be used for ordinal data or numerical data.

Question 50

The left side of the box in a boxplot is the first quartile and the right side of the box in a boxplot is the third quartile, so the width of the box is the interquartile range.

Question 51

The coefficient of variation gives an indication of the magnitude of the standard deviation relative to the mean.

Question 52

The standard deviation is expressed in terms of the original units of measurement, but the variance is not.

Question 53

The value of the standard deviation will always exceed that of the variance.

Question 54

The width of the box in a boxplot is the mean of the data set.

Question 55

A courier company is reviewing their delivery times. The following descriptive statistics relates to this courier company. The mean time for package delivery is 5 hours, the first quartile is 4 hours, the third quartile is 17 hours. This means that the median must lie between 4 hours and 17 hours.

Question 56

While Chebyshev's theorem applies to any distribution, regardless of shape, the empirical rule applies only to distributions that are bell-shaped and symmetrical.

Question 57

The empirical rule states that the percentage of observations in a data set (provided that the data set has a bell-shaped and symmetric distribution) that fall within one standard deviation of their mean is
approximately 75%.

Question 58

There are no measures of variability for nominal data.

Question 59

The coefficient of variation is the standard deviation divided by the mean.

Question 60

The interquartile range is found by taking the difference between the 1st and 3rd quartiles and dividing that value by 2.

Question 61

What are the relative magnitudes of the mean, median and mode for a unimodal distribution that is:
a. symmetrical?
b. skewed to the left?
c. skewed to the right?

Question 62

The coefficient of determination measures the percentage of variation in the independent variable explained by the dependent variable.

Question 63

The least squares method is the method of deriving a linear equation between two numerical variables.

Question 64

The coefficient of correlation is the covariance divided by the standard deviation

Question 65

The coefficient of determination may range in values between negative one and positive one.

Question 66

The following data represent the numbers of bedrooms in a sample of 10 suburban houses in Melbourne: Use these data to answer the following question/s.
a. Compute the mean.
b. Compute the median.

Question 67

The shape of the distribution helps to determine the best measure of central location and variability in a data set.

Question 68

A basketball player has the following points for seven games: 20, 25, 32, 18, 19, 22, 30. Compute the following measures of central location and variability:
a. mean.
b. median.
c. standard deviation.
d. coefficient of variation.

Question 69

A sample of 25 families was asked how many pets they owned. Their responses are summarized in the following table.

a. Determine the mean, the median and the mode of the number of pets owned per family.
b. Describe briefly what each statistic in part (a) tells you about the data.

Question 70

A courier company is reviewing their delivery times. The following descriptive statistics relates to this courier company. The mean time for package delivery is 5 hours, the first quartile is 4 hours, the third quartile is 17 hours. This means that 50% of deliveries take more than 5 hours?

Question 71

The coefficient of determination lies between 0 and 1.

Question 72

The coefficient of correlation is the same value as the coefficient of determination.

Question 73

If the coefficient of correlation r = +1, then the best-fit linear equation will actually be satisfied by all of the data points.

Question 74

The correlation coefficient only measures the direction and strength of a linear relationship between two numerical variables.

Question 75

The coefficient of correlation indicates the direction and the strength of the linear relationship between two variables.

Question 76

When approximating descriptive measures for grouped data, the shape of the distribution within each class is ignored.

Question 77

Generally speaking, if two variables have a strong positive linear relationship, the covariance between them is equal to one.

Question 78

If the coefficient of correlation r = 0, then there is no linear relationship between the dependent variable y and the independent variable x.

Question 79

When approximating descriptive measures for grouped data, the sample mean can be obtained by making the assumption that the midpoint of each class closely approximates the mean of each class.

Question 80

Monthly rent data in dollars for a sample of 10 one-bedroom apartments in Perth are given below: a. Compute the sample monthly average rent.
b. Compute the sample median.
c. What is the mode?