Question

The mean deviation from the median for the following data is:

• A. \(0.75\)
• B. \(7.5\)
• C. \(0.65\)
• D. \(0.40\)

Hint:

Mean deviation about median is calculated using \(\frac{\sum f|x-M|}{N}\), where \(M\) is the median.

Answer 1

The Correct Option is A

Step 1: Determine the total number of observations.
N = 6 + 12 + 18 + 12 = 48.

Step 2: Locate the median.
Cumulative frequencies: 6, 18, 36, 48. Half of N is 24, which falls in the third class corresponding to x = 12. Hence the median is 12.

Step 3: Compute the mean deviation about the median.
M.D. = Σ f|x - Median|/N = [6|10-12| + 12|11-12| + 18|12-12| + 12|13-12|]/48 = [6(2) + 12(1) + 18(0) + 12(1)]/48 = (12 + 12 + 0 + 12)/48 = 36/48 = 0.75.

Step 4: Final conclusion.
The mean deviation about the median is 0.75.