What does standard deviation measure in a data set?

What does standard deviation measure in a data set?

• A. How spread out the data are around the mean.
• B. The mean value.
• C. The median.
• D. The sum of data points.

Answer: (A)

Standard deviation is a measure of dispersion, showing how far data points typically lie from the average value. It captures the spread of the data around the mean: a small spread means most values are close to the mean, while a large spread means values are more spread out. Technically, you compute it by measuring each value’s deviation from the mean, squaring those deviations, averaging them, and taking the square root. This process emphasizes larger deviations, so outliers can increase the standard deviation more than most other measures of spread. This concept is distinct from the mean itself (which is a central tendency indicating the typical value), the median (the middle value in ordered data), or the sum (the total of all values). So what standard deviation conveys is the typical distance from the mean — i.e., how spread out the data are.

Standard deviation is a measure of dispersion, showing how far data points typically lie from the average value. It captures the spread of the data around the mean: a small spread means most values are close to the mean, while a large spread means values are more spread out.

Technically, you compute it by measuring each value’s deviation from the mean, squaring those deviations, averaging them, and taking the square root. This process emphasizes larger deviations, so outliers can increase the standard deviation more than most other measures of spread.

This concept is distinct from the mean itself (which is a central tendency indicating the typical value), the median (the middle value in ordered data), or the sum (the total of all values). So what standard deviation conveys is the typical distance from the mean — i.e., how spread out the data are.