Deck 3: Numerical Descriptive Techniques

Question 1

If the median, median and mode are all equal, the histogram must be symmetric and bell shaped.

Answer 1

False

Question 2

Lily has been keeping track of what she spends to eat 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.

Answer 2

True

Question 3

The data set 10, 20, 30 has the same variance as the data set 100, 200, 300.

Answer 3

False

Question 4

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

Question 5

Suppose a sample of size 50 has a sample mean of 20. In this case, the sum of all observations in the sample is 1,000.

Question 6

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 7

$\mu$ is a population parameter and is a sample statistic.

Question 8

The median of a set of data is more representative than the mean when the mean is larger than most of the observations.

Question 9

The value of the mean times the number of observations equals the sum of the observations.

Question 10

In a histogram, the proportion of the total area which must be to the left of the median is more than 0.50 if the distribution is positively skewed.

Question 11

The Empirical Rule states that the percentage of observations in a data set (providing that the data set is bell shaped) that fall within one standard deviation of their mean is approximately 75%.

Question 12

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

Question 13

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

Question 14

The median of an ordered data set with 30 items would be the average of the 15^th and the 16^th observations.

Question 15

The mean is affected by extreme values but the median is not.

Question 16

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

Question 17

The difference between the largest and smallest observations in an ordered data set is called the range.

Question 18

In a histogram, the proportion of the total area which must be to the right of the mean is exactly 0.50 if the distribution is symmetric and unimodal.

Question 19

In a histogram, the proportion of the total area which must be to the left of the median is less than 0.50 if the distribution is negatively skewed.

Question 20

The mean is a measure of variability.

Question 21

The standard deviation is the positive square root of the variance.

Question 22

In symmetric data, the value for Q₂ is always halfway between Q₁ and Q₃.

Question 23

The range is considered the weakest measure of variability.

Question 24

If the distribution of a data set were perfectly symmetric, the distance from Q₁ to the median would always equal the distance from Q₃ to the median in a box plot.

Question 25

If two data sets have the same standard deviation, they must have the same coefficient of variation.

Question 26

Expressed in percentiles, the interquartile range is the difference between the 25^th and 75^th percentiles.

Question 27

The length of the box in a box plot portrays the interquartile range.

Question 28

The value for Q₃ can never be smaller than the value for Q₁.

Question 29

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

Question 30

The interquartile range will always exceed that of the range.

Question 31

The distance between the 25^th percentile and the median is always the same as the distance between the median and the 75^th percentile.

Question 32

If the observations are in the millions, a standard deviation of 10 would be considered small. If the observations are all less than 50, a standard deviation of 10 would be considered large.

Question 33

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

Question 34

The variance is more meaningful and easier to interpret compared to the standard deviation.

Question 35

A population with 200 elements has a variance of 20. From this information, it can be shown that the population standard deviation is 10.

Question 36

The coefficient of variation is a measure of variability.

Question 37

The first and second quartiles of a data set can never be equal.

Question 38

Quartiles divide the observations in a data set into four parts with the same amount of data in each part.

Question 39

If two data sets have the same range, the distances from the smallest to largest observations in both sets will be the same.

Question 40

The units for the variance are the same as the units for the original data (for example, feet, inches, etc.).

Question 41

The coefficient of correlation r is a number that indicates the direction and the strength of the linear relationship between the dependent variable y and the independent variable x.

Question 42

A box plot is a graphical representation of the 5-number summary.

Question 43

If the coefficient of correlation r = -.81, the standard deviations of x and y are 20 and 25, respectively, then cov(x, y) must be -405.0.

Question 44

The variance is a measure of the linear relationship between two variables

Question 45

The interquartile range is an interval of numbers starting at Q₁ and ending at Q₃.

Question 46

If the coefficient of correlation r = 0, there can be no relationship whatsoever between the dependent variable y and the independent variable x.

Question 47

The 5-number summary consists of the smallest observation, the first quartile, the median, the third quartile, and the largest observation.

Question 48

The interquartile range is a measure of variability in a set of data.

Question 49

Expressed in percentiles, the fifth decile is the 50^th percentile or the median.

Question 50

The line drawn within the box of a box plot always represents the mean.

Question 51

Three measures of the linear relationship between x and y are the coefficient of correlation, the coefficient of determination, and the coefficient of variation.

Question 52

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

Question 53

The advantage that the coefficient of correlation has over the covariance is that the former has set lower and upper limits.

Question 54

If the standard deviation of x is 18, the covariance of x and y is 120, the coefficient r = 0.90, then the standard deviation of y is 54.87.

Question 55

If , , n = 12, and the slope equals 0.5, then the y-intercept of the least squares line is b₀ = 276.08.

Question 56

Percentiles can be converted into quintiles and deciles, where quintiles divide the data into fifths and deciles divide the data into tenths.

Question 57

The line drawn within the box of a box plot always represents the median.

Question 58

If the standard deviations of x and y are 12.5 and 10.8, respectively, and the covariance is 118.8, then the coefficient of correlation r is 0.88.

Question 59

Generally speaking, if two variables are unrelated, the covariance will be a number close to zero.

Question 60

If the covariance of x and y is 26.16, and the standard deviation of x is 32.7, then the slope of the least squares line is b₁ =.80.

Question 61

In a perfectly symmetric bell shaped "normal" distribution:

A) the mean equals the median.
B) the median equals the mode.
C) the mean equals the mode.
D) All of these choices are true.

Question 62

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

A) The median.
B) The mean.
C) The range.
D) The interquartile range.

Question 63

Which measure of central location is meaningful when the data are ordinal?

A) The mean
B) The median
C) The mode
D) All of these choices are meaningful for ordinal data.

Question 64

Which of the following is a measure of variability?

A) The interquartile range
B) The variance
C) The coefficient of variation
D) All of these choices are true.

Question 65

Which of these measures of central location is not sensitive to extreme values?

A) The mean
B) The median
C) The mode
D) All of these choices are true.

Question 66

When the standard deviation is expressed as a percentage of the mean, the result is the coefficient of correlation.

Question 67

If the coefficient of correlation r = $\pm$ 1, then the best-fit linear equation will actually include all of the observations.

Question 68

In a positively skewed distribution:

A) the median equals the mean.
B) the median is less than the mean.
C) the median is larger than the mean.
D) the mean can be larger or smaller than the median.

Question 69

A perfect straight line sloping upward would produce a correlation coefficient value of 1.0.

Question 70

Which of the following statistics is a measure of central location?

A) The mean
B) The median
C) The mode
D) All of these choices are true.

Question 71

If two data sets have the same range:

A) the distances from the smallest to largest observations in both sets will be the same.
B) the smallest and largest observations are the same in both sets.
C) both sets will have the same standard deviation.
D) both sets will have the same interquartile range.

Question 72

Which of the following statements about the mean is not always correct?

A) The sum of the deviations from the mean is zero.
B) Half of the observations are on either side of the mean.
C) The mean is a measure of the central location.
D) The value of the mean times the number of observations equals the sum of all observations.

Question 73

Which of the following summary measures is sensitive to extreme values?

A) The median
B) The interquartile range
C) The mean
D) The first quartile

Question 74

Which of the following statements is true?

A) When the distribution is positively skewed, mean > median > mode.
B) When the distribution is negatively skewed, mean < median < mode.
C) When the distribution is symmetric and unimodal, mean = median = mode.
D) When the distribution is symmetric and bimodal, mean = median = mode.

Question 75

Which measure of central location can be used for both interval and nominal variables?

A) The mean
B) The median
C) The mode
D) All of these choices are true.

Question 76

The Empirical Rule states that the approximate percentage of measurements in a data set (providing that the data set has a bell shaped distribution) that fall within two standard deviations of their mean is approximately:

A) 68%.
B) 75%.
C) 95%.
D) 99%.

Question 77

Which of the following statements about the median is not true?

A) It is more affected by extreme values than the mean.
B) It is a measure of central location.
C) It is equal to Q₂.
D) It is equal to the mode in a bell shaped distribution.

Question 78

In a histogram, the proportion of the total area which must be to the left of the median is:

A) exactly 0.50.
B) less than 0.50 if the distribution is negatively skewed.
C) more than 0.50 if the distribution is positively skewed.
D) unknown.

Question 79

Which of the following statements is true for the following observations: 9, 8, 7, 9, 6, 11, and 13?

A) The mean, median and mode are all equal.
B) Only the mean and median are equal.
C) Only the mean and mode are equal
D) Only the median and mode are equal.

Question 80

In a histogram, the proportion of the total area which must be to the right of the mean is:

A) less than 0.50 if the distribution is negatively skewed.
B) exactly 0.50.
C) more than 0.50 if the distribution is positively skewed.
D) exactly 0.50 if the distribution is symmetric and unimodal.