Question

​​Calculate mean,variance,standard deviation for the following distribution
​Classes- 30-40 40-50 50-60 60-70 70-80 80-90 90-100
frequency 3 7 12 15 8 3 2

Answer 1

Classes	Class mark $\left(x_i\right)$	frequency $\left(f_i\right)$	$x_i$$f_i$	$\left|x_i-\overline{x}\right|$	${\left(x_i-\overline{x}\right)}^2$
30-40	35	3	105	27	729
40-50	45	7	315	17	289
50-60	55	12	660	7	49
60-70	65	15	975	3	9
70-80	75	8	600	13	169
80-90	85	3	255	23	529
90-100	95	2	190	33	1089

$$\begin{gathered} classmark=\frac{lowerlimit+upperlimit}{2} \\ \overline{x}=\frac{\sum _1^n{x}_i{f}_i}{\sum _1^n{f}_i}=\frac{3100}{50}=62 \\ s\tan dardeviation=\frac{\sum _1^n\left|x_i-\overline{x}\right|}{\sum _1^n{f}_i}=\frac{123}{50}=2.46 \\ Vriance{\sigma }^2=\frac{\sum _1^n{\left(x_i-\overline{x}\right)}^2}{\sum _1^n{f}_i}=\frac{2862}{50}=57.24 \end{gathered}$$