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Mathematics · Statistics · NCERT Examples

Example 8

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Mathematics · Chapter 13 · NCERT Examples

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NCERT Example

Example 8

median · missing frequencies

The median of the following distribution is 525 and the total frequency is 100. Find x and y.

Class

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

Solution

Board-exam working:

Using the total frequency:

2+5+x+12+17+20+y+9+7+4=1002+5+x+12+17+20+y+9+7+4=100
x+y=24(1)x+y=24\qquad\text{(1)}

Since 525 lies in 500–600, that is the median class.

l=500,f=20,cf=36+x,h=100,n2=50l=500,\quad f=20,\quad cf=36+x,\quad h=100,\quad \frac n2=50
525=500+50−(36+x)20×100525=500+\frac{50-(36+x)}{20}\times100
25=5(14−x)=70−5x25=5(14-x)=70-5x
5x=45⇒x=95x=45\Rightarrow x=9

Substitute in equation (1).

9+y=24⇒y=159+y=24\Rightarrow y=15

Final answer

x=9,y=15\boxed{x=9,\qquad y=15}