Question 1

The mean is a better measure of central tendency than the median when there are outliers.

Accepted Answer

When there are outliers, the mean can become skewed because it is influenced by extreme values. The median, on the other hand, is less affected by outliers and provides a better representation of the typical value. Therefore, the median is a better measure of central tendency in the presence of outliers.

Question 2

The median and the 50^th percentile are always equal.

Accepted Answer

The median is the value separating the higher half from the lower half of a data sample, and the 50th percentile is the value below which 50% of the data falls, making them equivalent measures of central tendency.

Question 3

The mode is the most useful measure of central tendency if the data is ordinal.

Accepted Answer

The mode is the most useful measure of central tendency for ordinal data because it identifies the most frequently occurring value or category, which can be useful in describing the characteristic that is most typical or common in a dataset. Other measures of central tendency, such as the mean or median, may not be as useful for ordinal data because they rely on numerical values and may not accurately represent the underlying order of the data.

Question 4

In a positively skewed distribution,the mode is greater than the median.

Accepted Answer

In a positively skewed distribution, the tail of the distribution is pointing towards the higher values, which means that there are more low values and a few very high values. Therefore, the mean is generally greater than the median, and the mode may or may not be greater than the median. In some cases, the mode may coincide with the median, especially if the high values cluster together. In other cases, the mode may be smaller than the median, especially if there are outliers that pull the median towards the high end.

Question 5

The interquartile range measures the spread of the lower 50% of data values.

Accepted Answer

The interquartile range measures the spread of the middle 50% of data values, between the first and third quartiles.

Question 6

A variable measured at the interval or ratio level can have more than one arithmetic mean.

Accepted Answer

A variable measured at the interval or ratio level has only one arithmetic mean, as the arithmetic mean is a unique measure of central tendency calculated by summing all the values and dividing by the count of values.

Question 7

Quartiles and percentiles are two of the most popular measures of dispersion.

Accepted Answer

Quartiles and percentiles are actually measures of central tendency, specifically, measures of position. Measures of dispersion include standard deviation, variance, and range.

Question 8

The coefficient of variation (CV)is a measure of relative dispersion that expresses the standard deviation as a percentage of the mean (provided the mean is positive).

Accepted Answer

The statement correctly defines the coefficient of variation as a measure of relative dispersion that expresses the standard deviation as a percentage of the mean, given that the mean is positive. Therefore, the answer is true.

Question 9

Consider two possible investments with the same expected rate of return.Over the past several months,investment A has had an average closing price of $14.00 and a standard deviation of $4.00.Investment B has had an average closing price of $58.00 and a standard deviation of $15.00.The market value of investment A fluctuates relatively more than investment B.

Accepted Answer

The standard deviation of investment A is 28.57% of its average closing price ($4/$14), while the standard deviation of investment B is 25.86% ($15/$58). This means that investment A has a higher degree of fluctuation relative to its average closing price compared to investment B. Therefore, the statement is true - the market value of investment A fluctuates relatively more than investment B, even though they have the same expected rate of return.

Question 10

The variance of a set of data can never be negative.

Accepted Answer

The variance is defined as the average of the squared differences from the mean. The squared differences can never be negative, so the sum of squared differences and the variance can never be negative as well.

Question 11

If the mean is greater than the median,then the distribution is skewed to the right.

Accepted Answer

If the mean is greater than the median, it indicates that the distribution has a longer tail on its right side, which means it is skewed to the right.

Question 12

Suppose that the average score on an exam is 73 with a standard deviation of 2.According to Chebyshev's theorem,at least 60% of the scores are in the interval between 70 and 76.

Accepted Answer

The answer of Suppose that the average score on an...

Question 13

Suppose you have a set of data which has a bell-shaped histogram.Compare the interquartile range with the range from one standard deviation below the mean to one standard deviation above the mean.The interquartile range is smaller.

Accepted Answer

A bell-shaped histogram indicates a normal distribution. In a normal distribution, the interquartile range covers 50% of the data from the 25th percentile to the 75th percentile. One standard deviation below the mean to one standard deviation above the mean covers approximately the same proportion of data (68%). However, the interquartile range covers only the middle 50% of the data, while the range of one standard deviation below/above the mean includes the entire 68% of the data, making it larger than the interquartile range.

Question 14

For any distribution,the number of values above the mean and below it is the same.

Accepted Answer

The statement is not always true because the distribution of values in a dataset can be skewed, meaning there could be more values above or below the mean, depending on the nature of the distribution.

Question 15

The median,the second quartile,and the 50th percentile are all the same.

Accepted Answer

The median, second quartile, and 50th percentile all refer to the same value in a dataset - the value that is exactly in the middle when the data is arranged in numerical order. Therefore, the statement is true.

Question 16

The advantage of Chebyshev's theorem is that its applicability extends to any population regardless of its shape.However,it is within this guarantee that its major drawback lies.

Accepted Answer

Chebyshev's theorem provides a general guideline and applies to all types of population irrespective of their distribution shape. However, the drawback is that the result obtained from this theorem is often very broad with a wide range of possible values, making it less informative.

Question 17

For salaries of $108,000,$102,000,$52,000,$105,000,107,000 and $101,000,the arithmetic mean would be an appropriate measure of central tendency.

Accepted Answer

The answer of For salaries of $108,000,$102,000,$52,000,$105,000,107,000 and $101,000,the arithmetic...

Question 18

For any distribution,the empirical rule estimates that approximately 95% of the observations will fall with two standard deviations of the mean.

Accepted Answer

The answer of For any distribution,the empirical rule estimates that...

Question 19

If the population variance σ² is unknown,a sample variance s² is a better estimator of σ² if the denominator is s² formula is (n - 1)rather than n.

Accepted Answer

This is true. Using the denominator (n-1) in the formula for sample variance results in an unbiased estimator for population variance. Using the denominator n makes the estimator biased, as it underestimates the population variance.

Question 20

Any set of ordinal,interval or ratio level data may only have one mode.

Accepted Answer

This statement is false. A set of data may have multiple modes, especially if there are more than two values that occur with equal frequency.

Quiz 2: Describing Data: Numerical