Weekly average wages of $25$ workers in a factory is Rs. $800$ and SD is Rs. $100$ . The other group of $70$ workers has mean wages of Rs. $1200$ and SD of Rs. $250$ . Find the combined mean and SD.

1099.5, 200

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1095.73, 287

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1094.73, 282.32

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1090.22, 300

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Solution

The correct option is C $1094.73, 282.32$
$n_{1} = 25, {¯ x}_{1} = 800, σ_{1} = 100,$ $n_{2} = 70, {¯ x}_{2} = 1200, σ_{2} = 250$
$¯ x = \frac{n_{1} {¯ x}_{1} + n_{2} {¯ x}_{2}}{n_{1} + n_{2}} = \frac{25 \times 800 + 70 \times 1200}{95} = 1094.73$ $R s .$
$d_{1} = {¯ x}_{1} - ¯ x = 800 - 1094.73 = - 294.73$ $R s .$
$d_{2} = {¯ x}_{2} - ¯ x = 1200 - 1094.73 = 105.27$ $R s .$
$σ^{2} (n_{1} + n_{2}) = n_{1} (σ_{1}^{2} + d_{1}^{2}) + n_{2} (σ_{2}^{2} + d_{2}^{2})$
$σ^{2} (95) = 25 \times (10000 + 86865.77) + 70 \times (6250 + 11081.77)$
$σ^{2} = 79709.13$
$σ = 282.32$ $R s .$

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Weekly average wages of 25 workers in a factory is Rs. 800 and SD is Rs. 100. The other group of 70 workers has mean wages of Rs. 1200 and SD of Rs. 250. Find the combined mean and SD.

Weekly average wages of $25$ workers in a factory is Rs. $800$ and SD is Rs. $100$ . The other group of $70$ workers has mean wages of Rs. $1200$ and SD of Rs. $250$ . Find the combined mean and SD.