Median class is 20-30 (median $\approx27.86$); computing $f_i\times|x_i-\text{median}|$ for each class and dividing the total by $N=50$ gives mean deviation $\approx10.34$.

$N = 6+8+14+16+4+2 = 50$

Step 1 — Median: $N/2 = 25$. The cumulative frequency first reaches/exceeds 25 in the class 20-30 (cf before $=14$, $f=14$), so this is the median class, with $l=20$, $h=10$:

$\text{Median} = l + \dfrac{\tfrac N2 - cf}{f}\times h = 20 + \dfrac{25-14}{14}\times10 = 20 + \dfrac{110}{14} = 20 + \dfrac{55}{7} = \dfrac{195}{7} \approx 27.857$

Step 2 — Absolute deviations $|x_i - \text{Median}|$ (using Median $=195/7$):

| $x_i$ | $|x_i - 195/7|$ | $f_i$ | $f_i|x_i-\text{Med}|$ |

|---|---|---|---|

| 5 | $160/7$ | 6 | $960/7$ |

| 15 | $90/7$ | 8 | $720/7$ |

| 25 | $20/7$ | 14 | $280/7 = 40$ |

| 35 | $50/7$ | 16 | $800/7$ |

| 45 | $120/7$ | 4 | $480/7$ |

| 55 | $190/7$ | 2 | $380/7$ |

Sum $= \dfrac{960+720+280+800+480+380}{7} = \dfrac{3620}{7}$

Step 3 — Mean deviation about the median:

$\text{M.D.} = \dfrac{1}{N}\sum f_i|x_i-\text{Median}| = \dfrac{3620/7}{50} = \dfrac{3620}{350} = \dfrac{362}{35} \approx 10.34$

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