1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# The daily expenditure of 100 families are given below. Calculate f1 and f2 if the mean daily expenditure is ₹188. Expenditure (in ₹) 140−160 160−180 180−200 200−220 220−240 Number of families 5 25 f1 f2 5

Open in App
Solution

## The given data is shown as follows: Expenditure (in ₹) Number of families (fi) Class mark (xi) fixi 140−160 5 150 750 160−180 25 170 4250 180−200 f1 190 190f1 200−220 f2 210 210f2 220−240 5 230 1150 Total ∑ fi = 35 + f1 + f2 ∑ fixi = 6150 + 190f1 + 210f2 Sum of the frequencies = 100 $⇒\sum _{i}{f}_{i}=100\phantom{\rule{0ex}{0ex}}⇒35+{f}_{1}+{f}_{2}=100\phantom{\rule{0ex}{0ex}}⇒{f}_{1}+{f}_{2}=100-35\phantom{\rule{0ex}{0ex}}⇒{f}_{1}+{f}_{2}=65\phantom{\rule{0ex}{0ex}}⇒{f}_{2}=65-{f}_{1}....\left(1\right)$ Now, The mean of given data is given by $\overline{x}=\frac{\sum _{i}{f}_{i}{x}_{i}}{\sum _{i}{f}_{i}}\phantom{\rule{0ex}{0ex}}⇒188=\frac{6150+190{f}_{1}+210{f}_{2}}{100}\phantom{\rule{0ex}{0ex}}⇒18800=6150+190{f}_{1}+210{f}_{2}\phantom{\rule{0ex}{0ex}}⇒18800-6150=190{f}_{1}+210{f}_{2}\phantom{\rule{0ex}{0ex}}⇒12650=190{f}_{1}+210\left(65-{f}_{1}\right)\left[\mathrm{from}\left(1\right)\right]\phantom{\rule{0ex}{0ex}}⇒12650=190{f}_{1}-210{f}_{1}+13650\phantom{\rule{0ex}{0ex}}⇒20{f}_{1}=13650-12650\phantom{\rule{0ex}{0ex}}⇒20{f}_{1}=1000\phantom{\rule{0ex}{0ex}}⇒{f}_{1}=50$ If f1 = 50, then f2 = 65 − 50 = 15 ​Thus, the value of f1 is 50 and f2 is 15.

Suggest Corrections
8
Join BYJU'S Learning Program
Related Videos
Mean
MATHEMATICS
Watch in App
Join BYJU'S Learning Program