Asked by Holden Aldridge on Mar 10, 2024
Verified
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.
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.
Coefficient of Variation
A statistical measure of the dispersion of data points in a data set, relative to its mean, expressed as a percentage.
Standard Deviation
A measure of the dispersion or spread of a set of data points relative to its mean, indicating how spread out the data points are.
- Identify the differences among several measures of variability and their exposure to extreme measurements.
Verified Answer
BP
Briana Perez
Mar 10, 2024
Final Answer :
D
Explanation :
The range equals the difference between the maximum and minimum values in the data set, and in this case, they are all the same (8-8=0), so the range equals 0.
The standard deviation is a measure of the spread or dispersion of a data set, and when all values in the data set are the same, the standard deviation equals 0.
The coefficient of variation is the ratio of the standard deviation to the mean, and when the standard deviation is 0 (as it is in this case), the coefficient of variation also equals 0. Therefore, all of these choices are true.
The standard deviation is a measure of the spread or dispersion of a data set, and when all values in the data set are the same, the standard deviation equals 0.
The coefficient of variation is the ratio of the standard deviation to the mean, and when the standard deviation is 0 (as it is in this case), the coefficient of variation also equals 0. Therefore, all of these choices are true.
Learning Objectives
- Identify the differences among several measures of variability and their exposure to extreme measurements.