Find the mean of the following distribution by Assumed Mean Method: | |
Class interval | Frequency |
10 ? 20 | 8 |
20 ? 30 | 7 |
30 ? 40 | 12 |
40 ? 50 | 23 |
50 ? 60 | 11 |
60 ? 70 | 13 |
70 ? 80 | 8 |
80 ? 90 | 6 |
90 ? 100 | 12 |
Answer:
Class interval Frequency \[({{f}_{i}})\] \[{{X}_{i}}\] \[{{d}_{i}}={{X}_{i}}-55\] \[{{f}_{i}}{{d}_{i}}\] 10 ? 20 8 15 \[\text{ }40\] \[\text{ }320\] 20 ? 30 7 25 \[\text{ }30\] \[\text{ }210\] 30 ? 40 12 35 \[\text{ }20\] \[\text{ }240\] 40 ? 50 23 45 \[\text{ }10\] \[\text{ }230\] 50 ? 60 11 55 0 0 60 ? 70 13 65 10 130 70 ? 80 8 75 20 160 80 ? 90 6 85 30 180 90 ? 100 12 95 40 480 \[\sum{{{f}_{i}}}=100\] \[\sum{{{f}_{i}}{{d}_{i}}}=-50\] Let \[A=55\] Mean \[=A+\frac{\sum{{{f}_{i}}{{d}_{i}}}}{\sum{{{f}_{i}}}}=55+\left( \frac{-50}{100} \right)\] \[=55-\frac{50}{100}=55-0.5=54.5\]
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