Q.Find the mean deviation about the median for the following data: 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21.

Concept: Mean Deviation About Median — we first find the median, then average the absolute deviations from it.

Step 1 – Arrange data in ascending order:

3, 3, 4, 5, 7, 9, 10, 12, 18, 19, 21

$n = 11$ (odd), so median is the $\left(\frac{11+1}{2}\right)^{\text{th}} = 6^{\text{th}}$ term.

Step 2 – Identify median:

The 6th term is $9$.

Median $M = 9$.

Step 3 – Compute absolute deviations from median: …

Understanding Mean Deviation About the Median

The median is the middle value that splits ordered data into two equal halves. Mean deviation about the median reports the average absolute distance of each observation from that middle value.

Step-by-Step Solution

1. Arrange the data in ascending order

There are $n = 11$ observations (odd).

2. Find the median

For odd $n$, the median is the $\left(\dfrac{n+1}{2}\right)^{\text{th}}$ value $= 6^{\text{th}}$ value $= 9$.

3. Absolute deviations from the median

| $x_i$ | $|x_i - 9|$ |

|-------|-------------| …