Concept: Mean Deviation About Median – we find the median class, compute the median, then take the absolute deviations of class midpoints from that median, weighted by frequencies.

Step 1 – Cumulative frequencies and median class

Cumulative frequencies: 4, 9, 12, 18, 20.

$N = 20$, so $\frac{N}{2} = 10$. The median lies in the class $12-18$ (cumulative 12 first exceeds 10).

Step 2 – Compute the median

Median $M = L + \frac{\frac{N}{2} - cf}{f} \times h$

$L = 12$, $cf = 9$, $f = 3$, $h = 6$

$M = 12 + \frac{10 - 9}{3} \times 6 = 12 + 2 = 14$

Step 3 – Mean deviation about median

Midpoints: 3, 9, 15, 21, 27. …

Step 1: Cumulative frequencies and median class

$N = 20$, so $\tfrac{N}{2} = 10$. The first cumulative frequency $\ge 10$ is $12$, so the median class is $12\text{–}18$.

Step 2: Median

Step 3: Midpoints and absolute deviations from the median