Monthly pocket money of students of a class is given in the following frequency distribution: | |||||
Pocket money (in Rs.) | 100 ? 125 | 125 ? 150 | 150 ? 175 | 175 ? 200 | 200 ? 225 |
Number of students | 14 | 8 | 12 | 5 | 11 |
Find mean pocket money using step deviation method. |
Answer:
Pocket Money (in Rs.) No. of Students \[({{f}_{i}})\] \[{{X}_{i}}\] \[{{d}_{i}}=\frac{{{X}_{i}}-162.5}{25}\] \[{{f}_{i}}{{d}_{i}}\] 100 ? 125 14 112.5 \[2\] \[28\] 125 ? 150 8 137.5 \[1\] \[8\] 150 ? 175 12 a = 162.5 0 0 175 ? 200 5 187.5 1 5 200 ? 225 11 212.5 2 22 \[\sum{{{f}_{i}}=50}\] \[\sum{{{f}_{i}}{{d}_{i}}=-9}\] Mean \[=a+\frac{\sum{{{f}_{i}}{{d}_{i}}}}{\sum{{{f}_{i}}}}\times h\] \[=162.5+\left( \frac{-9}{50}\times 25 \right)\] \[=162.5-4.5=Rs.\,\,158\]
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