question_answer

For helping poor girls of their class, students saved pocket money as shown in the following table:
Money saved (in Rs.)	5 ? 7	7 ? 9	9 ? 11	11 ? 13	13 ? 15
Number of students	6	3	9	5	7
Find mean and median for this data.

Answer:

Money saved (in Rs.)	No, of Students \[({{f}_{i}})\]	\[{{X}_{i}}\]	\[{{d}_{i}}=\frac{{{X}_{i}}-10}{2}\]	\[{{f}_{i}}{{d}_{i}}\]	\[c.f.\]
5 ? 7	6	6	\[2\]	\[-12\]	6
7 ? 9	3	8	\[1\]	\[-3\]	9
9 ? 11	9	\[a=10\]	0	0	18
11 ? 13	5	12	1	5	23
13 ? 15	7	14	2	14	30
	\[\sum{{{f}_{i}}=30}\]			\[\sum{{{f}_{i}}{{d}_{i}}=4}\]
(i)         Mean \[=a+\frac{\sum{{{f}_{i}}{{d}_{i}}}}{\sum{{{f}_{i}}}}\times h\]
\[=10+\frac{4}{30}\times 2=10+0.27\]
\[=Rs.\,10.27\]
(ii)                  \[N=\sum{{{f}_{i}}=30}\]
\[\frac{N}{2}=\frac{30}{2}=15,\]
\[\therefore \] Median class is 9 ? 11.
Median \[=l+\frac{\frac{N}{2}-F}{f}\times h\]
\[=9+\frac{15-9}{9}\times 2=9+\frac{6}{9}\times 2\]
\[=9+1.33=Rs.\,\,10.33\]