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 respectively. If the variance of all the 30 numbers in the two sets is 13, then is equal to [2023]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
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 $σ^{2}$ respectively. If the variance of all the 30 numbers in the two sets is 13, then $σ^{2}$ is equal to [2023]

1 10

2 11

3 12

4 9

Ans.
(1)

Combine variance

$= \frac{n_{1} σ_{1}^{2} + n_{2} σ_{2}^{2}}{n_{1} + n_{2}} + \frac{n_{1} n_{2} {(m_{1} - m_{2})}^{2}}{{(n_{1} + n_{2})}^{2}}$

$\Rightarrow 13 = \frac{15 \cdot 14 + 15 \cdot σ^{2}}{30} + \frac{15 \cdot 15 {(12 - 14)}^{2}}{30 \times 30}$

$\Rightarrow 13 = \frac{14 + σ^{2}}{2} + \frac{4}{4} \Rightarrow σ^{2} = 10$

Want Us to Email you About Special Offers & Updates?