Find mean and standard deviation (S.D.) of the following frequency distribution: Class-Interval 70-75, 75-80, 80-85, 85-90, 90-95, 95-100, 100-105 with Frequency 3, 4, 7, 6, 5, 3, 2 respectively.

Question

Accepted Answer

>

> [!TLDR]
> Use the step-deviation method with assumed mean $A=87.5$ and class width $h=5$: find $\sum f_id_i$ and $\sum f_id_i^2$, then apply the mean and variance formulas.
>
> Class midpoints and deviations $d_i=\dfrac{x_i-A}{h}$ with $A=87.5$, $h=5$:
>
> | Class | Midpt $x_i$ | $f_i$ | $d_i$ | $f_id_i$ | $f_id_i^2$ |
> |---|---|---|---|---|---|
> |70-75|72.5|3|-3|-9|27|
> |75-80|77.5|4|-2|-8|16|
> |80-85|82.5|7|-1|-7|7|
> |85-90|87.5|6|0|0|0|
> |90-95|92.5|5|1|5|5|
> |95-100|97.5|3|2|6|12|
> |100-105|102.5|2|3|6|18|
>
> $n=\sum f_i = 30$, $\sum f_id_i = -7$, $\sum f_id_i^2 = 85$
>
> **Mean:**
> $\bar x = A+h\cdot\dfrac{\sum f_id_i}{n} = 87.5+5	imes\dfrac{-7}{30} = 87.5-1.1\overline{6} \approx 86.33$
> …

Q.Find mean and standard deviation (S.D.) of the following frequency distribution: Class-Interval 70-75, 75-80, 80-85, 85-90, 90-95, 95-100, 100-105 with Frequency 3, 4, 7, 6, 5, 3, 2 respectively.

Concept understanding — Variance and Standard Deviation of Data

Variance and Standard Deviation of Data

Class	Midpt $x_i$	$f_i$	$d_i$	$f_id_i$	$f_id_i^2$
70-75	72.5	3	-3	-9	27
75-80	77.5	4	-2	-8	16
80-85	82.5	7	-1	-7	7
85-90	87.5	6	0	0	0
90-95	92.5	5	1	5	5
95-100	97.5	3	2	6	12
100-105	102.5	2	3	6	18

Q.Find mean and standard deviation (S.D.) of the following frequency distribution: Class-Interval 70-75, 75-80, 80-85, 85-90, 90-95, 95-100, 100-105 with Frequency 3, 4, 7, 6, 5, 3, 2 respectively.

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