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Frequency Distributions

Find the miss...

Question

Find the missing frequencies $f_{1}$ and $f_{2}$ if the mean of the following data is $78$ and total frequency is $50$ .
Class Interval 50-60 60-70 70-80 80-90 90-100 Total
Frequency 8 $f_{1}$ 12 $f_{2}$ 13 50

A

f_{1} = 4

and

f_{2} = 13

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B

f_{1} = 5

and

f_{2} = 12

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C

f_{1} = 6

and

f_{2} = 11

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D

f_{1} = 7

and

f_{2} = 10

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Solution

The correct option is C $f_{1} = 6$ and $f_{2} = 11$
$C I$ $f_{i}$ $x_{i}$ $f_{i} x_{i}$
$50 - 60$ $8$ $55$ $440$
$60 - 70$ $f_{1}$ $65$ $65 f_{1}$
$70 - 80$ $12$ $75$ $900$
$80 - 90$ $f_{2}$ $85$ $85 f_{2}$
$90 - 100$ $13$ $95$ $1235$
$\sum f_{i} = 33 + f_{1} + f_{2}$ $\sum f_{i} x_{i} = 2575 + 65 f_{1} + 85 f_{2}$
$\Rightarrow$ $\sum f_{i} = 50$ [ Given ]
$∴$ $33 + f_{1} + f_{2} = 50$
$∴$ $f_{1} = 17 - f_{2}$ ------ ( 1 )
$\Rightarrow$ $M e a n = \frac{\sum f_{i} x_{i}}{\sum f_{i}}$
$78 = \frac{2575 + 65 f_{1} + 85 f_{2}}{50}$ $3900 = 2575 + 65 f_{1} + 85 f_{2}$
$1325 = 65 f_{1} + 85 f_{2}$
$1325 = 65 (17 - f_{2}) + 85 f_{2}$
$1325 = 1105 - 65 f_{2} + 85 f_{2}$
$220 = 20 f_{2}$
$∴$ $f_{2} = \frac{220}{20} = 11$ ----- ( 2 )
Substituting value of ( 2 ) in ( 1 ),
$∴$ $f_{1} = 17 - 11 = 6$
$∴$ $f_{1} = 6$ and $f_{2} = 11$

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Similar questions

Q. The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency

f_{1}

f_{2}

.

Class	0-20	20-40	40-60	60-80	80-100	100-120
Frequency	5	$f_{1}$	10	$f_{2}$	7	8

Q. The mean of the following frequency table is

57.6

. But the frequencies

f_{1}

f_{2}

are missing. Find the value of missing frequencies

f_{1}

f_{2}

Class Interval	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	$100 - 120$	Total
Frequency	$7$	$f_{1}$	$12$	$f_{2}$	$8$	$5$	$50$

Q. The mean of the following frequency table 50. But the frequencies

f_{1}

f_{2}

in class 20-40 and 60-80 are missing. Find the missing frequencies.

Class:	0-20	20-40	40-60	60-80	80-100	Total
Frequency:	17	$f_{1}$	32	$f_{2}$	19	120

Q. The mean of the following frequency distribution of

62.8

and the sum of all frequencies is

50

Compute the sum of missing frequencies

f_{1}

f_{2}

Class	0 - 20	20 - 40	40 - 60	60 - 80	80 - 100	100 - 120
Frequency	$5$	$f_{1}$	$10$	$f_{2}$	$7$	$8$

Class	0-20	20-40	40-60	60-80	80-100
Frequency	19	$f_{1}$	32	$f_{2}$	19	Total 120

Mean of the above frequency table is given as

50

f_{1}

f_{2}

.

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