Find the mean deviation about the median for the following data: Class $0$–$10$, $10$–$20$, $20$–$30$, $30$–$40$, $40$–$50$, $50$–$60$ with Frequency $6, 7, 15, 16, 4, 2$ respectively.

**OR**

Using short cut method, find the mean, variance and standard deviation for the followi

Question

Find the mean deviation about the median for the following data: Class $0$–$10$, $10$–$20$, $20$–$30$, $30$–$40$, $40$–$50$, $50$–$60$ with Frequency $6, 7, 15, 16, 4, 2$ respectively.

**OR**

Using short cut method, find the mean, variance and standard deviation for the following data: Class $25$–$35$, $35$–$45$, $45$–$55$, $55$–$65$, $65$–$75$ with Frequency $64, 132, 153, 140, 51$ respectively.

Accepted Answer

>

> [!TLDR]
> Find $N$, the median class via cumulative frequency, the median itself, then $\sum f|x_i-	ext{median}|$ divided by $N$.
>
> | Class | Freq $f$ | Midpoint $x$ | c.f. |
> |---|---|---|---|
> | 0–10 | 6 | 5 | 6 |
> | 10–20 | 7 | 15 | 13 |
> | 20–30 | 15 | 25 | 28 |
> | 30–40 | 16 | 35 | 44 |
> | 40–50 | 4 | 45 | 48 |
> | 50–60 | 2 | 55 | 50 |
>
> $N = 6+7+15+16+4+2 = 50$
>
> **Median:** $N/2=25$. The first cumulative frequency $\ge 25$ is $28$, in class $20$–$30$ (so this is the median class): $L=20,\ cf=13$ (c.f. before median class), $f=15,\ h=10$.
>
> $	ext{Median} = L+\dfrac{\frac{N}{2}-cf}{f}	imes h = 20+\dfrac{25-13}{15}	imes 10 = 20+\dfrac{12}{15}	imes10 = 20+8 = 28$
>
> **Mean deviation about the median:**
> …

Class	Freq $f$	Midpoint $x$	c.f.
0–10	6	5	6
10–20	7	15	13
20–30	15	25	28
30–40	16	35	44
40–50	4	45	48
50–60	2	55	50

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