Question

3 select all the statements that are true about standard deviation. a. it is a measure of center. b. it is a measure of variability. c. it is the same as the mad. d. it is calculated using the mean. e. it is calculated using the median.

Explanation:

• Standard deviation measures how spread out data is (variability), not the center (mean, median, mode are measures of center). So A is false and B is true.
• Mean - Absolute - Deviation (MAD) and standard deviation are different measures. MAD is the average of the absolute - value of the differences between data points and the mean, while standard deviation involves squaring the differences. So C is false.
• The formula for standard deviation of a sample $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$ and for a population $\sigma=\sqrt{\frac{\sum_{i = 1}^{N}(x_{i}-\mu)^{2}}{N}}$ uses the mean ($\bar{x}$ for sample, $\mu$ for population), not the median. So D is true and E is false.

Answer:

B. It is a measure of variability.
D. It is calculated using the mean.