question_answer

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 \[=a+\frac{\sum{{{f}_{i}}{{d}_{i}}}}{\sum{{{f}_{i}}}}\times h\]
\[=162.5+\left( \frac{-9}{50}\times 25 \right)\]
\[=162.5-4.5=Rs.\,\,158\]