Question 1

The arithmetic mean is the sum of the quantitative observations divided by the total number of observations.

Accepted Answer

This is the definition of the arithmetic mean.

Question 2

According to the Empirical Rule, about 95% of the observations lie within plus and minus 2.00 standard deviations.

Accepted Answer

The Empirical Rule states that about 68% of the observations lie within plus and minus 1.00 standard deviations, about 95% of the observations lie within plus and minus 2.00 standard deviations, and about 99.7% of the observations lie within plus and minus 3.00 standard deviations. Therefore, the statement is true.

Question 3

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

Accepted Answer

A set of ordinal-, interval-, or ratio-level data may have multiple modes.

Question 4

The mode is the value of the observation that appears most frequently.

Accepted Answer

The statement is true. The mode is the value that appears most frequently in a set of observations.

Question 5

For a set of data arranged or sorted in numerical order, the value of the observation in the center is called the weighted mean.

Accepted Answer

The value in the center of a set of data arranged in numerical order is called the median. The weighted mean takes into account the frequency or weight of each observation and is calculated by multiplying each observation by its weight, adding them up, and dividing by the total weight.

Question 6

For any distribution, there are an equal number of values above and below the mean.

Accepted Answer

The mean is a measure of central tendency, but it does not guarantee an equal number of values above and below it. This property is true for the median, not the mean.

Question 7

Variation describes the degree of dispersion in the data.

Accepted Answer

This is true. Variation refers to how spread out data is, and it is often measured using statistics such as the range, variance, or standard deviation.

Question 8

The mean deviation is the sum of the absolute differences between each value and the median.

Accepted Answer

The mean deviation can be calculated based on the mean or the median, but it is more commonly associated with the mean, where it is the average of the absolute differences between each value and the mean of the dataset.

Question 9

The sum of the deviations from the mean for the set of numbers 4, 9, and 5 will equal zero.

Accepted Answer

The mean of the set of numbers is (4+9+5)/3 = 6.

The deviations from the mean are:

- 4-6 = -2
- 9-6 = 3
- 5-6 = -1

The sum of these deviations is (-2) + 3 + (-1) = 0. Therefore, the statement is true.

Question 10

The variance is the mean of the sum of the squared deviations between each observation and the median.

Accepted Answer

The variance is the mean of the sum of the squared deviations between each observation and the mean, not the median.

Question 11

Extremely high or low scores affect the value of the median.

Accepted Answer

The median is the middle value in a data set when it is ordered from smallest to largest, and it is not affected by the magnitude of extremely high or low scores.

Question 12

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

Accepted Answer

This is correct. The standard deviation is indeed the positive square root of the variance.

Question 13

For any data set, which measures of central location have only one value?

Accepted Answer

Only the mean or median can have only one value as a measure of central tendency. The mode refers to the most frequently occurring value and may have multiple values, while standard deviation is a measure of dispersion and not central tendency.

Question 14

The sum of the deviations of each data value from this measure of central location will always be zero.

Accepted Answer

This is a property of the mean. By definition, the mean is the sum of all the data values divided by the number of data values. Therefore, the deviation of each value from the mean can be either positive or negative, but their sum will always be zero.

Question 15

In a sample of 10 people, 3 persons earn $8 an hour, 6 earn $9 an hour, and 1 earns $12 an hour. The weighted mean hourly wage is $9.

Accepted Answer

To calculate the weighted mean, we multiply each wage by its corresponding frequency (number of people earning that wage), add up these products and divide by the total number of people.

(3 * 8) + (6 * 9) + (1 * 12) = 8(3) + 9(6) + 12(1) = 24 + 54 + 12 = 90
Total number of people = 10

Weighted mean = 90/10 = $9

Question 16

Which measures of central location are not affected by extremely small or extremely large values?

Accepted Answer

The mode is the value that appears most frequently in a set of data, and the median is the middle value when a set of data is arranged in order. Both the mode and median are not affected by extremely small or extremely large values because they only consider the value that appears most frequently or the middle value. The mean and standard deviation are affected by extremely small or extremely large values, while the mode is not affected by extremely small values and the median is not affected by extremely small or extremely large values.

Question 17

According to Chebyshev's Theorem, 75% of the observations lie within plus and minus 2.00 average mean deviations.

Accepted Answer

Chebyshev's Theorem states that at least 75% of the observations lie within plus and minus 2.00 standard deviations from the mean, not average mean deviations. Therefore, the statement is false.

Question 18

For any data set, Chebyshev's Theorem estimates the proportion of observations that occurs within k standard deviations of the mean, where k is greater than 1.0.

Accepted Answer

Chebyshev's Theorem states that at least 1 - (1/k^2) proportion of observations will fall within k standard deviations of the mean, where k is greater than 1.0.

Question 19

In a company, the standard deviation of the ages of female employees is 6 years and the standard deviation of the ages of male employees is 10 years. These statistics indicate that the dispersion of age is greater for females than for males.

Accepted Answer

The greater standard deviation among male employees (10 years) compared to female employees (6 years) indicates that the dispersion of age is actually greater for males than for females.

Question 20

A value that is typical or representative of the data is referred to as a measure of central location.

Accepted Answer

This statement is true.

Quiz 3: Describing Data: Numerical Measures