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  •  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

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mansi

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