Question

13. The daily expenditure of 100 families are given below. Calculate fi and
have 861
Of
f, if the mean daily expenditure is ? 188.
140-160
160-180
180-200
200-220
220 240
Expenditure
(in)
Number of
families
5
25
2
CBSE 2014
C.11.
fround​

Answer 1

Answer:-

Expenditure in rupeesNumber of families(fi) Class mark(xi)fixi  140−1605 150 750 160−180 25 170 4250 180−200  f1190 190f1  200−220 f2 210 210f2 220−2405 230 1150  Total∑fi=35+f1+f2  ∑fixi=6150+190f1+210f2

Sum of the frequencies=100

⇒∑ifi=100

⇒35+f1+f

⇒f1+f2=100−35=65

⇒f2=65−f1       ........(1)

now, the mean of the given data is given by,

xˉ=∑ifi∑ifixi

⇒188=1006150+190f1+210f2

⇒18800−6160=190f1+210f2

⇒12650=190f1+210(65−f1) from (1)

⇒12650=190f1−210f1+13650

⇒20f1=1000

⇒f1=5