CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
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.)140160160180180200200220220240Number 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.


flag
Suggest Corrections
thumbs-up
47
BNAT
mid-banner-image