Question

If the variance of the data \( 2,3,5,8,12 \) is \( \sigma^2 \) and the mean deviation from the median for this data is \( M \), then \( \sigma^2 - M \) is:

• A. \( 10.2 \)
• B. \( 5.8 \)
• C. \( 10.6 \)
• D. \( 8.2 \)

Hint:

Variance measures spread, while mean deviation measures absolute dispersion.

Answer 1

The Correct Option is A

Observations: \( 2, 3, 5, 8, 12 \).
1. Mean calculation: \( {Mean} = \frac{2 + 3 + 5 + 8 + 12}{5} = 6 >
2. Variance calculation: \( \sigma^2 = 13.2 >
3. Median determination: The median is the middle value due to an odd number of observations: \( {Median} = 5 >
4. Mean Deviation about Median calculation: \( M = \frac{|2 - 5| + |3 - 5| + |5 - 5| + |8 - 5| + |12 - 5|}{5} = 3 >
5. Final result: \( \sigma^2 - M = 13.2 - 3 = 10.2 >