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The mean and standard deviation of 100 items are 50,5 and that of $\begin{array}{ll}150 \text { items are } 40,6 \text { respectively. } & [20] 4-1]\end{array}$
What is the combined mean of all 250 items?
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What is the combined mean of all 250 items?
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The correct answer is:
44
Mean of 100 items $=\overline{\mathrm{x}}_{100}=50$
Mean of 150 items $=\overline{\mathrm{x}}_{150}=40$
Standard deviation of 100 items $=\sigma_{100}=5$ Standard deviation of 150 items $=\sigma_{150}=6$
$\begin{aligned} \bar{x}_{250}=\frac{\mathrm{n}_{1} \bar{x}_{100}+\mathrm{n}_{2} \cdot \bar{x}_{150}}{\mathrm{n}_{1}+\mathrm{n}_{2}}=\frac{(100 \times 50)+(150 \times 40)}{100+150} \\=& \frac{11000}{250}=44 \end{aligned}$
Mean of 150 items $=\overline{\mathrm{x}}_{150}=40$
Standard deviation of 100 items $=\sigma_{100}=5$ Standard deviation of 150 items $=\sigma_{150}=6$
$\begin{aligned} \bar{x}_{250}=\frac{\mathrm{n}_{1} \bar{x}_{100}+\mathrm{n}_{2} \cdot \bar{x}_{150}}{\mathrm{n}_{1}+\mathrm{n}_{2}}=\frac{(100 \times 50)+(150 \times 40)}{100+150} \\=& \frac{11000}{250}=44 \end{aligned}$
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