If for a moderately symmetrical distribution mean deviation is 12, then the value of standard deviation is

Concept:

• The standard deviation (SD) measures the amount of variability, or dispersion, from the individual data values to the mean, while the standard error of the mean (SEM) or mean deviation measures how far the sample mean (average) of the data is likely to be from the true population mean.
• The SEM is always smaller than the SD.

• In a symmetrical distribution, mean deviation equals 4/5 of standard deviation.

Calculation:

Since the distribution is symmetrical,

⇒ Mean deviation = 4/5 of Standard deviation

⇒ 12 = (4/5) × Standard deviation

⇒ Standard deviation = 15

Hence, the value of the standard deviation is 15.