Calculate the Mean, Variance and Standard deviation for the following distribution: Classes 0–10, Frequency 5; Classes 10–20, Frequency 8; Classes 20–30, Frequency 15; Classes 30–40, Frequency 16; Classes 40–50, Frequency 6.

Question

Accepted Answer

>

> [!TLDR]
> Using the step-deviation method (assumed mean $A=25$, $h=10$) gives Mean $=27$, Variance $=132$, and SD $\approx11.49$.
>
> | Class | Frequency $f_i$ | Midpoint $x_i$ | $d_i=\dfrac{x_i-25}{10}$ | $f_id_i$ | $f_id_i^2$ |
> |---|---|---|---|---|---|
> | 0–10 | 5 | 5 | $-2$ | $-10$ | $20$ |
> | 10–20 | 8 | 15 | $-1$ | $-8$ | $8$ |
> | 20–30 | 15 | 25 | $0$ | $0$ | $0$ |
> | 30–40 | 16 | 35 | $1$ | $16$ | $16$ |
> | 40–50 | 6 | 45 | $2$ | $12$ | $24$ |
>
> $N=\sum f_i = 5+8+15+16+6=50$
>
> $\sum f_id_i = -10-8+0+16+12 = 10$
>
> $\sum f_id_i^2 = 20+8+0+16+24 = 68$
>
> **Mean:**
> $$\bar{x} = A + h	imes\dfrac{\sum f_id_i}{N} = 25 + 10	imes\dfrac{10}{50} = 25+2 = 27$$
>
> **Variance:** …

Q.Calculate the Mean, Variance and Standard deviation for the following distribution: Classes 0–10, Frequency 5; Classes 10–20, Frequency 8; Classes 20–30, Frequency 15; Classes 30–40, Frequency 16; Classes 40–50, Frequency 6.

Concept understanding — Variance and Standard Deviation of Data

Variance and Standard Deviation of Data

Class	Frequency $f_i$	Midpoint $x_i$	$d_i=\dfrac{x_i-25}{10}$	$f_id_i$	$f_id_i^2$
0–10	5	5	$-2$	$-10$	$20$
10–20	8	15	$-1$	$-8$	$8$
20–30	15	25	$0$	$0$	$0$
30–40	16	35	$1$	$16$	$16$
40–50	6	45	$2$	$12$	$24$

Q.Calculate the Mean, Variance and Standard deviation for the following distribution: Classes 0–10, Frequency 5; Classes 10–20, Frequency 8; Classes 20–30, Frequency 15; Classes 30–40, Frequency 16; Classes 40–50, Frequency 6.

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