Evaluation of Standard Deviation weakness?

Evaluation of Standard Deviation weakness?

• A. It ignores the mean
• B. It can be distorted by an extreme value
• C. It requires the data to be categorical
• D. It cannot be calculated for small samples

Answer: (B)

Standard deviation measures how much the data vary around the mean. Because it uses deviations from the mean and squares them, extreme values have a big influence, pulling the calculated spread higher than the rest of the data would suggest. That means an outlier can distort the standard deviation, giving a misleading impression of overall variability. This is why the statement that it can be distorted by an extreme value is the best match. Remember, it does depend on the mean and is a numerical measure, not for categoric data, and it can be calculated for small samples even though the estimate may be less stable.

Standard deviation measures how much the data vary around the mean. Because it uses deviations from the mean and squares them, extreme values have a big influence, pulling the calculated spread higher than the rest of the data would suggest. That means an outlier can distort the standard deviation, giving a misleading impression of overall variability. This is why the statement that it can be distorted by an extreme value is the best match.

Remember, it does depend on the mean and is a numerical measure, not for categoric data, and it can be calculated for small samples even though the estimate may be less stable.