The median of the following data is 525 - Find the values of x and y- if the total frequency is 100 - WhineClass Interval - Frequency lilhline0-100 - 2 Whline 100-200 - 5 11Hhine 200-300 - x Whline 300-400 - 12 Whline400-500 - 17 iNhline500-600 - 20 Whline 600-700 - y Whline 700-800 - 9 Wllhline800-900 - 7 Wlhline900-1000 - 4 Nhline lendarray -4 MARKS-

Concept: 1 Mark Application: 3 Marks [ Class Interval amp; Frequency amp; Cumulative frequency; 0 100 ...

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Standard X

Mathematics

Median for Grouped Data

The median of...

Question

The median of the following data is 525. Find the values of x and y, if the total frequency is 100.

$\begin{matrix} C l a s s I n t e r v a l & F r e q u e n c y 0 - 100 & 2 100 - 200 & 5 200 - 300 & x 300 - 400 & 12 400 - 500 & 17 500 - 600 & 20 600 - 700 & y 700 - 800 & 9 800 - 900 & 7 900 - 1000 & 4 \end{matrix}$ [4 MARKS]

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Solution

Concept: 1 Mark
Application: 3 Marks

$\begin{matrix} C l a s s I n t e r v a l & F r e q u e n c y & C u m u l a t i v e f r e q u e n c y 0 - 100 & 2 & 2 100 - 200 & 5 & 7 200 - 300 & x & 7 + x 300 - 400 & 12 & 19 + x 400 - 500 & 17 & 36 + x 500 - 600 & 20 & 56 + x 600 - 700 & y & 56 + x + y 700 - 800 & 9 & 65 + x + y 800 - 900 & 7 & 72 + x + y 900 - 1000 & 4 & 76 + x + y \end{matrix}$

It is given that n = 100

So, 76 + x + y = 100, i.e., x + y = 24---(1)

The median is 525, which lies in the class 500 - 600

So, l = 500, f = 20, $c_{f}$ = 36 + x, h = 100

Using the formula: Median $= l + (\frac{\frac{n}{2} - c_{f}}{f}) h$ , we get

i.e., $525 = 500 + (\frac{50 - 36 - x}{20}) \times 100$

i.e., $525 - 500 = (14 - x) \times 5$

i.e., $25 = 70 - 5 x$

i.e., $5 x = 70 - 25 = 45$

i.e., $x = 9$

From (1), we get $9 + y = 24$
y = 24 - 9= 15

The values of x,y are 9,15 respectively.

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Q. The median of the following data is

525

. Find the values of

x

and

y

, if the total frequency is

100

Class interval	Frequency
$0 - 100$	$2$
$100 - 200$	$5$
$200 - 300$	$x$
$300 - 400$	$12$
$400 - 500$	$17$
$500 - 600$	$20$
$600 - 700$	$y$
$700 - 800$	$9$
$800 - 900$	$7$
$900 - 1000$	$4$

The median of the following data is 525. Find the values of x and y, if the total frequency is 100.

$\begin{matrix} C l a s s I n t e r v a l & F r e q u e n c y 0 - 100 & 2 100 - 200 & 5 200 - 300 & x 300 - 400 & 12 400 - 500 & 17 500 - 600 & 20 600 - 700 & y 700 - 800 & 9 800 - 900 & 7 900 - 1000 & 4 \end{matrix}$ [4 MARKS]

Q. The median of the following data is 525. Find the missing frequency, if it is given that there are 100 observation in the data:

Class interval	Frequency	Class interval	Frequency
0−100 100−200 200−300 300−400 400−500	2 5 f₁ 12 17	500−600 600−700 700−800 800−900 900−1000	20 f₂ 9 7 4

Q. The median of the following data in

525

. Find the missing frequency, if it is given that there are

100

observations in the data:

Class interval	Frequency	Class interval	Frequency
0-100	$2$	500-600	$20$
100-200	$5$	600-700	$f_{2}$
200-300	$f_{1}$	700-800	$9$
300-400	$12$	800-900	$7$
400-500	$17$	900-1000	$4$

Find the mean of the given data.

$\begin{matrix} C l a s s i n t e r v a l & F r e q u e n c y 0 - 100 & 7 100 - 200 & 11 200 - 300 & 15 300 - 400 & 9 400 - 500 & 8 \end{matrix}$

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The median of the following data is 525. Find the values of x and y, if the total frequency is 100. Class IntervalFrequency0−1002100−2005200−300x300−40012400−50017500−60020600−700y700−8009800−9007900−10004 [4 MARKS]