QJEEM20Ma8786: JEE Main 2020 Mathematics - Class 11 JEEM20Ma8786 Solution: If the variance of the following frequency distribution :…

Question

Verified Solution • 2025–26 Session moderate

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____

Accepted Answer

x_i = midpoint of class interval

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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