An age-wise list of number of literate people in a block is prepared in the following table. There are total 100 people and their median age is 41.5 years. Information about two groups are missing, which are denoted by x and y. Find the value of x and y.

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Solution

Q.
An age-wise list of number of literate people in a block is prepared in the following table. There are total 100 people and their median age is 41.5 years. Information about two groups are missing, which are denoted by x and y. Find the value of x and y.

Age (in years) 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80

No. of literate people 15 $x$ 12 20 $y$ 8 10

Ans.
(15)

Age (in years) 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80

No. of literate people 15 $x$ 12 20 $y$ 8 10

cf 15 $15 + x$ $27 + x$ $47 + x$ $47 + x + y$ $55 + x + y$ $65 + x + y$

Here median age = 41.5 which belongs to 40 – 50

⇒ Median class is 40 – 50

$l = 40, c f = 27 + x, f = 20, h = 10$

$Median = l + (\frac{\frac{n}{2} - c f}{f}) \times h$

$\Rightarrow 41.5 = 40 + (\frac{50 - 27 - x}{20}) \times 10$

$\Rightarrow 41.5 - 40 = \frac{23 - x}{2}$

$\Rightarrow 3 = 23 - x \Rightarrow x = 23 - 3 = 20$

$\Rightarrow 65 + 20 + y = 100 \Rightarrow y = 100 - 85 = 15$

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