Name: Introduction to the Statistics
Uploaded: 2019-07-19
Duration: 4 min 50 s
Description: Statistics is a branch of Mathematics. In this video, we will learn the meaning of statistics and the classification of data. Let's watch this useful video t...

Question

The mean of the following frequency distribution is $57.6$ and the sum of the observations is $50$ . Find the missing frequencies $f_{1}$ and $f_{2}$ .

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

Accepted Answer

Given that, the mean of the given frequency distribution is $= \bar{x} = 57.6$ and the sum of all frequencies is $f_{2}$

If $x_{1}, x_{2}, x_{3}, . . . . . ., x_{n}$ are the class marks with corresponding frequencies $100 - 120$ respectively, then,

Mean $= \bar{x} = \frac{f_{1} x_{1} + f_{2} x_{2} + f_{3} x_{3} + . . . . . . . + f_{n} x_{n}}{f_{1} + f_{2} + f_{3} + . . . . . . . + f_{n}} = \frac{\sum f_{i} x_{i}}{\sum f_{i}}$

Class interval Frequency $(f_{i})$ Class Mark $(x_{i})$ $f_{1}$

$0 - 20$ $7$ $\frac{0 + 20}{2} = \frac{20}{2} = 10$ $70$

$20 - 40$ $f_{1}$ $30$ $30 f_{1}$

$40 - 60$ $12$ $50$ $600$

$60 - 80$ $f_{2}$ $70$ $70 f_{2}$

$80 - 100$ $8$ $90$ $720$

$100 - 120$ $5$ $110$ $550$

$\sum f_{i} = 32 + f_{1} + f_{2}$ $\sum f_{i} x_{i} = 1940 + 30 f_{1} + 70 f_{2}$

Given that, $\sum f_{i} = 50$

$\Rightarrow 32 + f_{1} + f_{2} = 50$

$\Rightarrow f_{1} + f_{2} = 50 - 32$

$\Rightarrow f_{1} = 18 - f_{2}$ --------- (i)

Since mean $= \bar{x} = \frac{\sum f_{i} x_{i}}{\sum f_{i}}$

$\Rightarrow 57.6 = \frac{1940 + 30 f_{1} + 70 f_{2}}{50}$

$\Rightarrow 2880 = 1940 + 30 (18 - f_{2}) + 70 f_{2}$ [From (i)]

$\Rightarrow 2880 - 1940 = 540 - 30 f_{2} + 70 f_{2}$

$\Rightarrow 940 - 540 = 40 f_{2}$

$\Rightarrow f_{2} = \frac{400}{40} = 10$

From (i), we get, $f_{1} = 18 - f_{2} = 18 - 10 = 8$ .

Hence, the value of $f_{1} = 8$ and $f_{2} = 10$ .

Class interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency	$12$	$16$	$6$	$7$	$9$

Class interval	$100 - 120$	$120 - 140$	$140 - 160$	$160 - 180$	$180 - 200$
Frequency	$10$	$20$	$30$	$15$	$5$

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
Number of students	$12$	$18$	$27$	$20$	$17$	$6$

Class interval	$50 - 70$	$70 - 90$	$90 - 110$	$110 - 130$	$130 - 150$	$150 - 170$
Frequency	$18$	$12$	$13$	$27$	$8$	$22$

Class interval	$0 - 50$	$50 - 100$	$100 - 150$	$150 - 200$	$200 - 250$	$250 - 300$
Frequency	$17$	$35$	$43$	$40$	$21$	$24$

The mean of the following frequency distribution is $57.6$ and the sum of the observations is $50$ . Find the missing frequencies $f_{1}$ and $f_{2}$ .

Class interval $0 - 20$ $20 - 40$ $40 - 60$ $60 - 80$ $80 - 100$ $100 - 120$

Frequency $7$ $f_{1}$ $12$ $f_{2}$ $8$ $5$

Important Questions on Statistics

Learn and Prepare for any exam you want !

Class interval	$0 - 20$	$0 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
Frequency	$15$	$18$	$21$	$29$	$17$

The mean of the following frequency distribution is 57.6 and the sum of the observations is 50. Find the missing frequencies f1 and f2. Class interval 0-20 20-40 40-60 60-80 80-100 100-120 Frequency 7 f1 12 f2 8 5

Important Questions on Statistics

Learn and Prepare for any exam you want !

The mean of the following frequency distribution is $57.6$ and the sum of the observations is $50$ . Find the missing frequencies $f_{1}$ and $f_{2}$ .

Class interval $0 - 20$ $20 - 40$ $40 - 60$ $60 - 80$ $80 - 100$ $100 - 120$

Frequency $7$ $f_{1}$ $12$ $f_{2}$ $8$ $5$