JEE MAIN - Mathematics (2020 - 4th September Evening Slot - No. 2)
If the variance of the following frequency
distribution :
Class : 10–20 20–30 30–40
Frequency : 2 x 2
is 50, then x is equal to____
Class : 10–20 20–30 30–40
Frequency : 2 x 2
is 50, then x is equal to____
Answer
4
Explanation
xi = midpoint of class interval
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Variance($$\sigma^{2})$$$$ =\frac{\sum f_{i}\left( x_{i}-\bar{x} \right)^{2} }{\sum f_{i}} $$
Also, $$\bar{x} =\frac{\sum f_{i}x_{i}}{\sum f_{i}} $$
= $$\frac{30+25x+70}{2+2+x} $$ = 25
Given, Variance = 50
$$ \therefore $$ 50 = $$\frac{200+0+200}{2+2+x} $$
$$ \Rightarrow $$ x = 4
Variance($$\sigma^{2})$$$$ =\frac{\sum f_{i}\left( x_{i}-\bar{x} \right)^{2} }{\sum f_{i}} $$
Also, $$\bar{x} =\frac{\sum f_{i}x_{i}}{\sum f_{i}} $$
= $$\frac{30+25x+70}{2+2+x} $$ = 25
Given, Variance = 50
$$ \therefore $$ 50 = $$\frac{200+0+200}{2+2+x} $$
$$ \Rightarrow $$ x = 4
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