The mean of two samples of series 50 and 100 are 53.7 and 52.3 respectively. Find the mean of combine sample.
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To perform combined mean calculations quickly without a calculator:
- Simplify the sample sizes into ratios:
\[ n_1 : n_2 = 50 : 100 = 1 : 2 \]
- Calculate using the simplified weights:
\[ \bar{x}_{12} = \frac{1(53.7) + 2(52.3)}{1 + 2} = \frac{53.7 + 104.6}{3} = \frac{158.3}{3} \approx 52.767 \]
This simplified method avoids working with large numbers.