Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  •  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 <img alt="\sigma^{2}" src="https://entrancecorner.oncode

 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 \sigma^{2} respectively. If the variance of all the 30 numbers in the two sets is 13 , then \sigma^{2}is equal to :

Option: 1

12


Option: 2

10


Option: 3

11


Option: 4

9


Answers (1)

best_answer

Combine\, var.=\frac{\mathrm{n}_{1} \sigma^{2}+\mathrm{n}_{2} \sigma^{2}}{\mathrm{n}_{1}+\mathrm{n}_{2}}+\frac{\mathrm{n}_{1} \mathrm{n}_{2}\left(\mathrm{~m}_{1}-\mathrm{m}_{2}\right)^{2}}{\left(\mathrm{n}_{1}+\mathrm{n}_{2}\right)}
13=\frac{15 \cdot 14+15 \cdot \sigma^{2}}{30}+\frac{15 \cdot 15(12-14)^{2}}{30 \times 30}
13=\frac{14+\sigma^{2}}{2}+\frac{4}{4}
\sigma^{2}=10

Posted by

mansi

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Latest Question