Question

Which one of the following is NOT a correct statement?

• A. The standard deviation is greater than or equal to the mean deviation (about mean)
• B. The variance is expressed in the same units as the units of observation
• C. The value of standard deviation changes by a change of scale.
• D. The sum of squares of deviations is minimum when taken from the mean

Hint:

Variance is always expressed in squared units, not in the same units as the data.

Answer 1

The Correct Option is B

The variance is the average of the squared deviations from the mean, so it is expressed in square units of the units of observation. Therefore, the statement that the variance is expressed in the same units as the units of observation is incorrect. The correct answer is option (b).

Step 1: Standard Deviation and Mean Deviation.
The standard deviation is always greater than or equal to the mean deviation. This is because the sum of the absolute deviations (mean deviation) is less than or equal to the square root of the sum of squared deviations (standard deviation).

Step 2: The Units of Variance.
Variance is calculated as the average of squared deviations, so its units are the square of the units of observation, unlike the standard deviation, which is in the same units as the data.

Step 3: Scale Effect on Standard Deviation.
The value of the standard deviation changes with scale. If we scale the data by a factor, the standard deviation is also scaled by the same factor. Thus, the correct answer is option (b).