Question 1

Weights of Teachers
The following data represent the weights in pounds of a sample of 25 teachers: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
-{Weights of Teachers Narrative} Which is a better measure of variability in the weights of the teachers, the standard deviation or the coefficient of variation?

Accepted Answer

The answer of Weights of Teachers
The following data represent the...

Question 2

Is a standard deviation of 10 a large number indicating great variability, or is it small number indicating little variability? To answer this question correctly, one should look carefully at the value of the:
A) mean.
B) standard deviation.
C) coefficient of variation.
D) mean dividing by the standard deviation.

Accepted Answer

The coefficient of variation (C) is the correct answer because it is a measure that indicates the extent of variability in relation to the mean of the population. It is calculated as the ratio of the standard deviation to the mean, and it provides a standardized measure of dispersion of a probability distribution or frequency distribution. This is useful for comparing the degree of variation from one data series to another, even if the means are drastically different from each other.

Question 3

____________________ uses both the mean and the standard deviation to interpret standard deviation for histograms of any shape.

Accepted Answer

The answer of ____________________ uses both the mean and the...

Question 4

There are three statistics used to measure variability in a data set; the range, the ____________________, and the ____________________.

Accepted Answer

The answer of There are three statistics used to measure...

Question 5

The ____________________ is the square root of the ____________________.

Accepted Answer

The answer of The ____________________ is the square root of...

Question 6

Which of the following statements is true regarding the data set 8, 8, 8, 8, and 8?
A) The range equals 0.
B) The standard deviation equals 0.
C) The coefficient of variation equals 0.
D) All of these choices are true.

Accepted Answer

- The range equals the difference between the largest and smallest values in the data set. In this case, the range is 8 - 8 = 0. Therefore, statement A is true.
- The standard deviation is a measure of how spread out the data is from the mean. Since all values in the data set are identical, there is no deviation from the mean, and the standard deviation is 0. Therefore, statement B is true.
- The coefficient of variation is a measure of relative variability and is calculated as the standard deviation divided by the mean, expressed as a percentage. Since the standard deviation is 0 and the mean is 8, the coefficient of variation is 0%. Therefore, statement C is also true.

Question 7

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.

Accepted Answer

All of these choices are measures of variability. The interquartile range measures the spread of the middle 50% of a data set, the variance measures the average distance of each point from the mean, and the coefficient of variation measures the ratio of the standard deviation to the mean, indicating the relative variability of a data set.

Question 8

The following data represent the number of children in a sample of 10 families from a certain community: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2.
a.
Compute the range.
b.
Compute the variance.
c.
Compute the standard deviation.
d.
Compute the coefficient of variation.
e.
Explain why in this case range > variance > standard deviation > coefficient of variation.

Accepted Answer

The answer of The following data represent the number of...

Question 9

A basketball player has the following points for seven games: 20, 25, 32, 18, 19, 22, and 30.Compute the following measures of variability.
a.
Standard deviation
b.
Coefficient of variation
c.
Compare the standard deviation and coefficient of variation and use them to discuss the variability in the data.

Accepted Answer

The answer of A basketball player has the following points...

Question 10

Weights of Teachers
The following data represent the weights in pounds of a sample of 25 teachers: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
-{Weights of Teachers Narrative} Compute the sample variance and sample standard deviation.

Accepted Answer

The answer of Weights of Teachers
The following data represent the...

Question 11

According to the Empirical Rule, if the data form a bell shaped normal distribution, approximately ____________________ percent of the observations will be contained within 2 standard deviations around the mean.

Accepted Answer

The answer of According to the Empirical Rule, if the...

Question 12

Which of the following types of data has no measure of variability?
A) Interval data.
B) Nominal data.
C) Bimodal data.
D) None of these choices.

Accepted Answer

Nominal data is categorical data that cannot be ranked or ordered, so there is no way to calculate a measure of variability. Interval data can have variability measured through the use of the standard deviation, and bimodal data refers to a distribution with two peaks, which does have a measure of variability. Therefore, the best choice is B.

Question 13

The ____________________ is the least effective of all the measures of variability.

Accepted Answer

The answer of The ____________________ is the least effective of...

Question 14

Weights of Teachers
The following data represent the weights in pounds of a sample of 25 teachers: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.
-{Weights of Teachers Narrative} Compute the range and coefficient of variation.

Accepted Answer

The answer of Weights of Teachers
The following data represent the...

Question 15

According to the Empirical Rule, if the data form a bell shaped normal distribution approximately ____________________ percent of the observations will be contained within 3 standard deviations around the mean.

Accepted Answer

The answer of According to the Empirical Rule, if the...

Question 16

According to the Empirical Rule, if the data form a bell shaped normal distribution approximately ____________________ percent of the observations will be contained within 1 standard deviation around the mean.

Accepted Answer

The answer of According to the Empirical Rule, if the...

Question 17

A statistic that interprets the standard deviation relative to the size of the numbers in the data set is called the ____________________ of ____________________.

Accepted Answer

The answer of A statistic that interprets the standard deviation...

Question 18

The ____________________ uses both the mean and the standard deviation to interpret standard deviation for bell shaped histograms.

Accepted Answer

The answer of The ____________________ uses both the mean and...

Question 19

The smaller the spread of scores around the mean:
A) the smaller the variance of the data set.
B) the smaller the standard deviation of the data set.
C) the smaller the coefficient of variation of the data set.
D) All of these choices are true.

Accepted Answer

All of these statements are true because the spread of scores around the mean directly affects the variance, standard deviation, and coefficient of variation of a data set. A smaller spread indicates that the data points are closer to the mean, leading to a smaller variance and standard deviation. Since the coefficient of variation is a standardized measure of dispersion that takes into account the mean of the dataset, a smaller spread around the mean also results in a smaller coefficient of variation.

Question 20

The range, variance, standard deviation, and coefficient of variation are to be used only on ____________________ data.

Accepted Answer

The answer of The range, variance, standard deviation, and coefficient...

Quiz 4: Numerical Descriptive Techniques

Is a standard deviation of 10 a large number indicating great variability, or is it small number indicating little variability? To answer this question correctly, one should look carefully at the value of the:

____________________ uses both the mean and the standard deviation to interpret standard deviation for histograms of any shape.

There are three statistics used to measure variability in a data set; the range, the , and the .

The is the square root of the .

Which of the following statements is true regarding the data set 8, 8, 8, 8, and 8?

Which of the following is a measure of variability?

According to the Empirical Rule, if the data form a bell shaped normal distribution, approximately ____________________ percent of the observations will be contained within 2 standard deviations around the mean.

Which of the following types of data has no measure of variability?

The ____________________ is the least effective of all the measures of variability.

According to the Empirical Rule, if the data form a bell shaped normal distribution approximately ____________________ percent of the observations will be contained within 3 standard deviations around the mean.

According to the Empirical Rule, if the data form a bell shaped normal distribution approximately ____________________ percent of the observations will be contained within 1 standard deviation around the mean.

A statistic that interprets the standard deviation relative to the size of the numbers in the data set is called the of .

The ____________________ uses both the mean and the standard deviation to interpret standard deviation for bell shaped histograms.

The smaller the spread of scores around the mean:

The range, variance, standard deviation, and coefficient of variation are to be used only on ____________________ data.