Mean deviation about the median (grouped data). Find the median from cumulative frequencies, then average the absolute deviations of the midpoints from it, weighted by frequency.

Cumulative frequencies: 6, 14, 28, 44, 48, 50; $N=50$, so $\dfrac{N}{2}=25$ lies in class 20–30.

Midpoints 5, 15, 25, 35, 45, 55 give …

The mean deviation about the median measures the average absolute distance of the observations from the median. For grouped data we first locate the median from cumulative frequencies, then average the absolute deviations of the class midpoints from it, weighted by frequency.

Step 1 — Cumulative frequencies and midpoints.

Total $N=50$.

Step 2 — Median.

$\dfrac{N}{2}=25$, which first falls in the class 20–30 ($cf=28$). With $L=20,\ cf=14,\ f=14,\ h=10$:

Step 3 — Weighted absolute deviations $f_i\lvert x_i-M\rvert$ (with $M=\tfrac{195}{7}$).