What does variance measure in a set of sample values?

What does variance measure in a set of sample values?

• A. The average of individual values
• B. The sum of squared deviations from the mean
• C. The maximum deviation within the set
• D. The total number of samples in the set

Answer: (B)

Variance measures the degree to which individual data points in a set differ from the mean of that set. It specifically quantifies how much the values in a sample deviate from the average value, reflecting the spread or dispersion of the data. The calculation of variance involves taking the differences between each value and the mean, squaring those differences to ensure that they are positive, and then averaging those squared differences by dividing by the number of data points (or by the number of data points minus one for sample variance). This process highlights how values are dispersed around the mean, making variance an essential statistic in quality control and data analysis. In contrast, the other choices do not accurately define variance. The average of individual values pertains to the mean rather than variance. The maximum deviation refers to a single largest difference, while the total number of samples simply counts how many data points are in the set. Therefore, the measurement that most directly captures the concept of how data values vary around the mean is indeed the sum of squared deviations from that mean.

Variance measures the degree to which individual data points in a set differ from the mean of that set. It specifically quantifies how much the values in a sample deviate from the average value, reflecting the spread or dispersion of the data.

The calculation of variance involves taking the differences between each value and the mean, squaring those differences to ensure that they are positive, and then averaging those squared differences by dividing by the number of data points (or by the number of data points minus one for sample variance). This process highlights how values are dispersed around the mean, making variance an essential statistic in quality control and data analysis.

In contrast, the other choices do not accurately define variance. The average of individual values pertains to the mean rather than variance. The maximum deviation refers to a single largest difference, while the total number of samples simply counts how many data points are in the set. Therefore, the measurement that most directly captures the concept of how data values vary around the mean is indeed the sum of squared deviations from that mean.