Question

Find the missing frequencies in the following frequency distribution table, if the total frequency is $100$ and mode is $46 \frac{2}{3}$ .

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$5$	$8$	$7$	$x$	$28$	$20$	$10$	$y$

Accepted Answer

Given,

$46 \frac{2}{3}$ The total frequency is $100$

$(2)$ Mode $=$ $46 \frac{2}{3}$

$10 - 20$ The frequency distribution table

Class $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$ $60 - 70$ $70 - 80$

Frequency $5$ $8$ $7$ $x$ $28$ $20$ $10$ $y$

We need to find the values $x, y$

The mode of grouped data is given by,

Mode $= l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h$ where,

$l =$ lower limit of the modal class,
$h =$ size of the class interval (assuming all class sizes to be equal),
$f_{1} =$ frequency of the modal class,
$f_{0} =$ frequency of the class preceding the modal class,
$f_{2} =$ frequency of the class succeeding the modal class.

Adding all frequencies we get, $8$

$\Rightarrow x + y = 22$ , $\Rightarrow x \leq 22, y \leq 22$

$\Rightarrow$ The highest frequency is $28$ and the modal class is $40 - 50$

$\Rightarrow l = 40, h = 10, f_{1} = 28, f_{0} = x, f_{2} = 20$

Substituting the values,

$40 + (\frac{28 - x}{2 \times 28 - x - 20}) \times 10 = 46 \frac{2}{3}$

$\Rightarrow (\frac{28 - x}{56 - x - 20}) \times 10 = 6 \frac{2}{3} = \frac{20}{3}$

$\Rightarrow (\frac{28 - x}{36 - x}) = \frac{2}{3}$

$\Rightarrow 2 (36 - x) = 3 (28 - x)$

$\Rightarrow 72 - 2 x = 84 - 3 x$

$\Rightarrow x = 12$

We know that $x + y = 22$

$\Rightarrow y = 22 - 12 = 10$

The complete frequency distribution table is given below:

Class $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$ $60 - 70$ $70 - 80$

Frequency $5$ $8$ $7$ $12$ $28$ $20$ $10$ $10$

Percentage of female teachers	$15 - 25$	$25 - 35$	$35 - 45$	$45 - 55$	$55 - 65$	$65 - 75$	$\Rightarrow 2 (36 - x) = 3 (28 - x)$
Number of States/U.T.	$6$	$11$	$7$	$4$	$4$	$2$	$1$

$x$	$10$	$30$	$50$	$70$	$90$
$y$	$17$	$f_{1}$	$32$	$f_{2}$	$19$	$Total 120$

Find the missing frequencies in the following frequency distribution table, if the total frequency is $100$ and mode is $46 \frac{2}{3}$ .

Class $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$ $60 - 70$ $70 - 80$

Frequency $5$ $8$ $7$ $x$ $28$ $20$ $10$ $y$

Important Questions on Statistics

Learn and Prepare for any exam you want !

Find the missing frequencies in the following frequency distribution table, if the total frequency is 100 and mode is 4623. Class 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Frequency 5 8 7 x 28 20 10 y

Important Questions on Statistics

Learn and Prepare for any exam you want !

Find the missing frequencies in the following frequency distribution table, if the total frequency is $100$ and mode is $46 \frac{2}{3}$ .

Class $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$ $60 - 70$ $70 - 80$

Frequency $5$ $8$ $7$ $x$ $28$ $20$ $10$ $y$