Question

The mean deviation about the median for the following data: \(6,3,4,9,2,7,11\) is:

• A. 1.89
• B. 2.57
• C. 3.14
• D. 6.23

Hint:

For mean deviation about median, sum absolute differences from median and divide by total number of data points.

Answer 1

The Correct Option is B

Step 1: Sort the data and locate the median.
Arranged in order: \(2,3,4,6,7,9,11\). The middle (4th) value is the median, \(6\).

Step 2: Pair up values symmetrically around the median and add each pair's total distance.
\[ (11-2) + (9-3) + (7-4) + |6-6| = 9+6+3+0 = 18 \]

Step 3: Divide by the number of observations.
There are 7 values in total, so
\[ \text{Mean deviation} = \frac{18}{7} \approx 2.57 \]

Step 4: State the final value.
\[ \boxed{2.57} \]