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 Rs. 188. Expenditure (in Rs.)140−160160−180180−200200−220220−240Number offamilies525f1f25

Open in App
Solution

## The given data is shown as follows: Expenditure (in Rs.) 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 ⇒ ∑fi = 100 ⇒ 35 + f1 + f2 = 100 ⇒ f1+f2 = 100-35 ⇒ f1+f2 = 65 ⇒f2 = 65 - f1 – – – – – – (1) Now, the mean of the given data is given by ¯x= ∑(fi×xi)/∑fi ⇒ 188 = 6150+190f1+210f2100 ⇒ 18800 = 6150 + 190f1 + 210f2 ⇒ 18800 - 6150 = 190f1 + 210f2 ⇒ 12650 = 190f1 + 210(65 - f1) [from (1)] ⇒ 12650 = 190f1 - 210f1 + 13650 ⇒ 20f1 = 13650 - 12650 ⇒ 20f1 = 1000 ⇒ f1 = 50 If f1 = 50, then f2 = 65 - 50 = 15 Thus, the value of f1 is 50 and f2 is 15.

Suggest Corrections
124
Join BYJU'S Learning Program
Related Videos
Mean
MATHEMATICS
Watch in App
Join BYJU'S Learning Program