Asked by michara delaney on Sep 23, 2024
Verified
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.
Variance
Variance measures the dispersion of a set of data points around their mean value, indicating how spread out the data is.
Standard Deviation
A statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.
Coefficient Of Variation
A measure of relative variability calculated as the standard deviation divided by the mean, often expressed as a percentage.
- Develop an understanding of the connection between standard deviation, variance, and the original measurement metrics.
Verified Answer
RN
Rusnah Ngadimin2 days ago
Final Answer :
D
Explanation :
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.
Learning Objectives
- Develop an understanding of the connection between standard deviation, variance, and the original measurement metrics.