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Q.

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 observations, then a+3b-5 is equal to_____.

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answer is 37.

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Detailed Solution

$x_{1}, x_{2}, . ......, x_{7} be the 7 observations$

$\frac{\sum x_{i}}{7} = 8 \Rightarrow \sum x_{i} = 56$
For 6 observation new mean $a = \frac{56 - 14}{6} = 7$
$\frac{\sum {x_{i}}^{2}}{7} - 64 = 16 \Rightarrow \sum {x_{i}}^{2} = 560$
For 6 observation new variance $b = \frac{560 - 14^{2}}{6} - 49 = \frac{35}{3}$
$∴ a + 3 b - 5 = 7 + 35 - 5 = 37$

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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 observations, then a+3b-5 is equal to_____.