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

In the following data the median of the runs scored by 60 top batsmen of the world in one-day international cricket matches is 5000. Find the missing frequencies

x

and

y

.

Runs scored	$2500 - 3500$	$3500 - 4500$	$4500 - 5500$	$5500 - 6500$	$6500 - 7500$	$7500 - 8500$
Number of batsmen	$5$	$x$	$y$	$12$	$6$	$2$

Accepted Answer

We prepare the cumulative frequency table, as shown below:

Runs scored Number of batsman $(f)$ Cumulative Frequency $(c f)$

$2500 - 3500$ $5$ $5$

$3500 - 4500$ $x$ $5 + x$

$4500 - 5500$ $y$ $5 + x + y$

$5500 - 6500$ $12$ $17 + x + y$

$6500 - 7500$ $6$ $23 + x + y$

$7500 - 8500$ $2$ $25 + x + y$

$x$

Let $3500 - 4500$ and $y$ be the missing frequencies of class intervals $3500 - 4500$ and $4500 - 5500$ respectively. Then, $25 + x + y = 60 \Rightarrow x + y = 35 . . . . (1)$
Median is $5000$ , which lies in $6$ . So, the median class is $4500 - 5500$ .
∴ $l = 4500, h = 1000, N = 60, f = y$ and $cf = 5 + x$ .

Now, median is given as,

$M = l + \frac{(\frac{N}{2} - cf)}{f} \times h$

$\Rightarrow 5000 = 4500 + \frac{(30 - 5 - x)}{y} \times 1000$

$\Rightarrow 500 = \frac{(25 - x)}{y} \times 1000$

$\Rightarrow y = 50 - 2 x$

$\Rightarrow 35 - x = 50 - 2 x$ [from $(1)$ ]

$\Rightarrow 2 x - x = 50 - 35$

$\Rightarrow x = 15$

$∴ y = 35 - x$ [from $(1)$ ]

$\Rightarrow y = 35 - 15$

$\Rightarrow y = 20$

“Note: Answer mentioned in the book is incorrect the correct answer is: $x = 15 & y = 20$ . ”
Hence, the missing frequency, $x = 15 & y = 20$ .

Class interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	Total
Frequency	$f_{1}$	$5$	$9$	$12$	$f_{2}$	$3$	$2$	$(1)$

Age (in years)	$19 - 25$	$26 - 32$	$33 - 39$	$40 - 46$	$47 - 53$	$54 - 60$
Frequency	$35$	$96$	$68$	$102$	$35$	$4$

Wages per day (in Rs)	$61 - 70$	$71 - 80$	$81 - 90$	$91 - 100$	$101 - 110$	$111 - 120$
No. of women workers	$5$	$15$	$20$	$30$	$20$	$8$

Class	$1 - 5$	$6 - 10$	$11 - 15$	$16 - 20$	$21 - 25$	$26 - 30$	$31 - 35$	$36 - 40$	$41 - 45$
Frequency	$7$	$10$	$16$	$32$	$24$	$16$	$11$	$5$	$2$

Marks	No. of students
Below $10$	$12$
Below $20$	$32$
Below $30$	$57$
Below $40$	$80$
Below $50$	$92$
Below $60$	$116$
Below $70$	$164$
Below $80$	$200$

Important Questions on Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive

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Class	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
Frequency	$25$	$16$	$28$	$20$	$5$

Height (in cm)	$150 - 155$	$155 - 160$	$160 - 165$	$165 - 170$	$170 - 175$
Number of students	$15$	$8$	$20$	$12$	$5$

In the following data the median of the runs scored by 60 top batsmen of the world in one-day international cricket matches is 5000. Find the missing frequencies x and y. Runs scored 2500-3500 3500-4500 4500-5500 5500-6500 6500-7500 7500-8500 Number of batsmen 5 x y 12 6 2

Important Questions on Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive

Learn and Prepare for any exam you want !