State True/ False:The daily expenditure of 100 families is given below. If the mean daily expenditure is Rs.57.6 and the sum of frequency is 50, then,

f
1

and
f
2

are respectively 8 and 10. Class0-2020-4040-6060-8080-100100-120Frequency7f112f285

Question

State True/ False:The daily expenditure of 100 families is given below. If the mean daily expenditure is Rs.57.6 and the sum of frequency is 50, then,

f
    1
   
    and 
    f
    2

are respectively 8 and 10. Class0-2020-4040-6060-8080-100100-120Frequency7f112f285

Accepted Answer

Consider the given table about the daily expenditure of 100 families,Class0-2020-4040-6060-8080-100100-120Frequency7f112f285It is given that the sum of frequencies is 50.

⇒7+
        f
        1
       
       +12+
        f
        2
       
       +8+5=50

⇒
        f
        2
       
       =18−
        f
        1
       
       ……(1)

The frequency distribution table for the given data is:Class intervalFrequencyfiMid-valuexifixi0-207107020-40f13030f140-60125060060-80f2=18-f1701260-70f180-100890720100-1205110550 50 3200-40f1We know that mean (x̲) = ∑fixi∑fi.Here,  ∑fixi=3200-40f1, ∑fi=50 and Mean (x̲) = 57.6.Therefore,

57.6=
        
         3200−40
          f
          1

50

⇒2880=3200−40
        f
        1

⇒40
        f
        1
       
       =320

⇒
        f
        1
       
       =8

Substituting the value of

f
    1

in equation (1):

f
        2
       
       =18−8

⇒
        f
        2
       
       =10

Hence, the value of

f
    1

and

f
    2

are 8 and 10 respectively.Thus, the given statement is true.Therefore, option 1 is correct.

State True/ False:

The daily expenditure of 100 families is given below. If the mean daily expenditure is Rs.57.6 and the sum of frequency is 50, then, $f 1 and f 2$ are respectively 8 and 10.

Class
0-20
20-40
40-60
60-80
80-100
100-120
Frequency
7
$f_{1}$
12
$f_{2}$
8
5

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Class	0-20	20-40	40-60	60-80	80-100	100-120
Frequency	7	$f_{1}$	12	$f_{2}$	8	5

Class interval	Frequency $f_{i}$	Mid-value $x_{i}$	$f_{i} x_{i}$
0-20	7	10	70
20-40	$f_{1}$	30	30 $f_{1}$
40-60	12	50	600
60-80	$f_{2} = 18 - f_{1}$	70	$1260 - 70 f_{1}$
80-100	8	90	720
100-120	5	110	550
	50		$3200 - 40 f_{1}$

State True/ False:The daily expenditure of 100 families is given below. If the mean daily expenditure is Rs.57.6 and the sum of frequency is 50, then, f 1 and f 2 are respectively 8 and 10. Class0-2020-4040-6060-8080-100100-120Frequency7f112f285