With $N=50$, the median class is $20$–$30$ (median $\approx 27.86$); the mean deviation about the median works out to $\approx 10.34$.

Given classes $0$-$10,\ldots,50$-$60$ with frequencies $6,8,14,16,4,2$.

Step 1 — find N and midpoints: $N = 6+8+14+16+4+2 = 50$. Midpoints: $5,15,25,35,45,55$.

Step 2 — locate the median class: Cumulative frequencies: $6,14,28,44,48,50$. $N/2 = 25$. The class where cumulative frequency first reaches/exceeds 25 is $20$-$30$ (cf $=28$), so this is the median class, with $l=20$, cf (before) $=14$, $f=14$, $h=10$.

Step 3 — compute the median: $\text{Median} = l + \dfrac{\frac{N}{2}-cf}{f}\times h = 20 + \dfrac{25-14}{14}\times 10 = 20 + \dfrac{110}{14} \approx 27.86$.

Step 4 — mean deviation about median: For each midpoint $x_i$, compute $|x_i - 27.86|$, multiply by $f_i$, and sum:

Step 5. Sum $\Sigma f_i|x_i-\text{Median}| \approx 517.14$. Mean deviation $= \dfrac{517.14}{50} \approx 10.34$.

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