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  • The mean and variance of 7 observations are 8 and 16 respectively. If one observation 14 is omitted and a and b are respectively mean and variance of remaining 6 observation, then a + 3b − 5

The mean and variance of 7 observations are 8 and 16 respectively. If one observation 14 is omitted and a and b are respectively mean and variance of remaining 6 observation, then a + 3b − 5 is equal to

Option: 1

37


Option: 2

__


Option: 3

__


Option: 4

__


Answers (1)

\begin{aligned} & \text { Mean of } 7 \text { observations }=\frac{\sum_{i=1}^7 x_i}{7} \\ & \Rightarrow \quad \sum_{i=1}^7 x_i=7 \times 8=56 \\ & \text { Variance }=\frac{\sum x_i^2}{\mathrm{n}}-(\bar{x})^2 \\ & \sum x_i^2=7(16+64)=560 \end{aligned}

If 14 is removed then

\begin{aligned} & \text { Mean }=\mathrm{a}=\frac{\sum_{i=1}^7 x_i-14}{6} \Rightarrow 6 a=56-14 \\ & \Rightarrow \mathrm{a}=7 \\ & \text { Variance }=b=\frac{\sum_{i=1}^7 x_i^2-(14)^2}{6}-49 \\ & \Rightarrow \quad 6 b=560-196-294 \\ & \Rightarrow \quad 6 b=70 \\ & \Rightarrow \quad 3 b=35 \\ & \therefore \quad a+3 b-5=7+35-5=37 \end{aligned}

Posted by

Ramraj Saini

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