Name: Mean of Grouped Data: Example
Uploaded: 2019-07-19
Duration: 5 min 16 s
Description: Want to find out how to calculate the mean of grouped data when the class intervals are different? Watch this interesting video and learn more!

Question

The median of the following data is $525$ . Find $x$ and $y$ if the sum of all frequencies is $100$ .

Class	$200 - 300$	$300 - 400$	$400 - 500$	$500 - 600$	$600 - 700$	$700 - 800$
Frequency	$16$	$x$	$17$	$20$	$15$	$y$

Accepted Answer

We observe that the classes of marks are continuous and are already arranged in ascending order.

First, we shall find the cumulative frequency (less than type) of the data.

Class $200 - 300$ $300 - 400$ $400 - 500$ $500 - 600$ $600 - 700$ $700 - 800$

Frequency $16$ $x$ $17$ $20$ $15$ $y$

Frequency (cumulative) $y$ $16 + x$ $33 + x$ $53 + x$ $68 + x$ $68 + x + y$

Given that the sum of all frequencies is $100$ .

Hence, $68 + x + y = 100$

$\Rightarrow x + y = 32$ ----- (i)

Also, given that the median of the following data is 525 . This means the median class is $500 - 600$ .

We know that the median is the value which lies inside the median class and is given by the formula $median = l + \frac{\frac{n}{2} - c . f .}{f} \times h$ , where,

$l =$ lower limit of the median class
$n =$ total number of observations
$c . f . =$ cumulative frequency of the class preceding the median class
$f =$ frequency of the median class
$h =$ size of the class (assuming that all classes have equal size)

Here, $l = 500, n = 100, c . f . = 33 + x, f = 20$ and $h = 100$ .

Hence, we have, $500 + \frac{\frac{100}{2} - (33 + x)}{20} \times 100 = 525$

$\Rightarrow \frac{\frac{100}{2} - (33 + x)}{20} \times 100 = 25$

$\Rightarrow 5 (17 - x) = 25$

$\Rightarrow 17 - x = 5$

$\Rightarrow x = 12$

From (i), we obtain, $x + y = 32$

$\Rightarrow 12 + y = 32$

$\Rightarrow y = 20$

Therefore, the required values are $x = 12$ and $y = 20$ .

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$\Rightarrow 17 - x = 5$	$60 - 70$	Total
Frequency	$x + y = 32$	$5$	$9$	$12$	$y$	$3$	$2$	$40$

Daily income (in $₹$ )	$100 - 120$	$120 - 140$	$140 - 160$	$160 - 180$	$180 - 200$
Number of workers	$12$	$14$	$8$	$6$	$10$

Number of letters	$1 - 4$	$4 - 7$	$7 - 10$	$10 - 13$	$13 - 16$	$16 - 19$
Number of surnames	$6$	$30$	$40$	$16$	$4$	$4$

Class	$5 - 15$	$15 - 25$	$25 - 35$	$35 - 45$	$45 - 55$	$55 - 65$	$65 - 75$
Frequency	$2$	$3$	$5$	$7$	$4$	$2$	$2$

Class interval	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$
Frequency	$10$	$8$	$12$	$24$	$6$	$25$	$15$

The median of the following data is $525$ . Find $x$ and $y$ if the sum of all frequencies is $100$ .

Class $200 - 300$ $300 - 400$ $400 - 500$ $500 - 600$ $600 - 700$ $700 - 800$

Frequency $16$ $x$ $17$ $20$ $15$ $y$

Important Questions on Statistics

Learn and Prepare for any exam you want !

Class	$0 - 30$	$30 - 60$	$60 - 90$	$90 - 120$	$120 - 150$
Frequency	$25$	$20$	$35$	$28$	$42$

Marks	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$	$45 - 50$
Number of students	$2$	$5$	$6$	$8$	$10$	$25$	$20$	$18$	$4$	$2$

The median of the following data is 525. Find x and y if the sum of all frequencies is 100. Class 200-300 300-400 400-500 500-600 600-700 700-800 Frequency 16 x 17 20 15 y

Important Questions on Statistics

Learn and Prepare for any exam you want !

The median of the following data is $525$ . Find $x$ and $y$ if the sum of all frequencies is $100$ .

Class $200 - 300$ $300 - 400$ $400 - 500$ $500 - 600$ $600 - 700$ $700 - 800$

Frequency $16$ $x$ $17$ $20$ $15$ $y$