Verified Solution • 2025–26 Session moderate

QJEEM23Ma1acb: JEE Main 2023 Mathematics - Class 11 JEEM23Ma1acb Solution: The mean and variance of a set of 15 numbers are 12 and 14…

The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of another set of 15 numbers are 14 and σ2 respectively. If the variance of all the 30 numbers in the two sets is 13 , then σ2 is equal to :

Multiple Choice Options

  • A 12
  • B 11
  • C 10
  • D 9

Step-by-Step Verified Solution

We know that if n1,n2n_1, n_2 are the sizes, Xˉ1,Xˉ2\bar{X}_1, \bar{X}_2 are the means and σ1,σ2\sigma_1, \sigma_2 are the standard deviation of the series, then the combine variance of the series.

σ2=n1σ12+n2σ22n1+n2+n1⋅n2(n1+n2)2(X¯1−X¯2)2⇒13=15×14+15×σ215+15+15×15(15+15)2(12−14)2⇒13=14+σ22+14×4⇒14+σ2=2×12⇒σ2=10

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