Concept: Mean Deviation About Median for a discrete frequency distribution.

Step 1 — Median. $N=8+6+2+2+2+6=26$ (even), so the median is the mean of the $13^{\text{th}}$ and $14^{\text{th}}$ values. The cumulative frequencies $8,14,16,18,20,26$ place both of these in $x_i=7$, so $M=7$.

Step 2 — Weighted absolute deviations from the median.

The mean deviation about the median measures the average absolute distance of the observations from the median. We first locate the median from the cumulative frequencies, then average the frequency-weighted absolute deviations — a standard NCERT Class 11 Maths Statistics calculation.

Step 1 — Total frequency.

Step 2 — Locate the median.

Since $N=26$ is even, the median is the average of the $13^{\text{th}}$ and $14^{\text{th}}$ observations. Build the cumulative frequencies:

The cumulative frequency first reaches (and exceeds) $13$ at $x_i=7$, and both the $13^{\text{th}}$ and $14^{\text{th}}$ observations lie there, so $M=7$.

Step 3 — Frequency-weighted absolute deviations from the median.