question_answer

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 \[=A+\frac{\sum{{{f}_{i}}{{d}_{i}}}}{\sum{{{f}_{i}}}}=55+\left( \frac{-50}{100} \right)\]
\[=55-\frac{50}{100}=55-0.5=54.5\]