Question

Find the mean of the following frequency distribution

Height from mean sea level	200	600	1000	1400	1800
No. of Villages	115	107	265	143	202

Answer 1

Let the assumed mean $A=1000,K=400$

Height $x_i$ No. of Villages $f_i$ $d_i=x_i-A$ $u_i=\frac{x_i-A}{K}$ $f_i{u}_i$

200 115 -800 -2 -230

600 107 -400 -1 -107

1000 265 0 0 0

1400 143 400 1 143

1800 202 800 2 404

832 $\sum f_i{u}_i=210$

$Mean=A+K\left(\frac{\sum f_i{u}_i}{\sum f_i}\right)=1000+\frac{400\times 210}{832}=1000+100.96=1100.96\simeq 1101$