Question

The weekly observation on cost of living Index in a ccrtain city for the year 2000 - 2001 are given below Compute the mean weekly cost of living index

Cost of Living Index	Number of weeks
140 - 150	5
150 - 160	10
160 - 170	20
170 - 180	9
180 - 190	6
190 - 200	2
Total	52

Answer 1

Let a = 175, h = 20

Calculation of Mean

Class

interval No.of

weeks $\left(f_i\right)$ mid-point

$\left(x_i\right)$

$u_i=\frac{x_i-175}{10}$a $f_i{u}_i$

140 - 150 5 145 -3 -15

150 - 160 10 155 -2 -20

160 - 170 20 165 -1 -20

170 - 180 9 175 0 0

180 - 190 9 175 1 6

180 - 190 6 185 1 6

190 - 200 2 195 2 4

Total 52 -45

$\overline{u}=\frac{1}{n}\sum _{i=l}^6{f}_i{u}_i=-\frac{45}{52}$

$\therefore \overline{x}=a+h\tilde{u}=175+10(-\frac{45}{52})$

$=175-\frac{450}{52}=175-8.65=166.35$

Hence mean weekly cost of living index

= 166.35

= 166.3 (approx)