Q.Find the mean deviation about the median for the data as under: $13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17$.

For the data $10,11,11,12,13,13,14,16,16,17,17,18$ (sorted), the median is $13.5$ and the mean deviation about the median is $\dfrac{7}{3}\approx2.33$.

The given data is: $13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17$ ($n=12$ values).

Step 1 — Sort the data:

$10, 11, 11, 12, 13, 13, 14, 16, 16, 17, 17, 18$

Step 2 — Find the median. Since $n=12$ is even, the median is the average of the $6$th and $7$th values:

$\text{Median} = \dfrac{13+14}{2} = 13.5$

Step 3 — Find $|x_i - \text{Median}|$ for each value:

| $x_i$ | $|x_i-13.5|$ |

|---|---|

| 10 | 3.5 |

| 11 | 2.5 |

| 11 | 2.5 |

| 12 | 1.5 |

| 13 | 0.5 |

| 13 | 0.5 |

| 14 | 0.5 | …