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
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.