question_answer

The frequency distribution of weekly pocket money received by a group of students is given below:
Pocket money in (Rs.)	More than or equal to 20	More than or equal to 40	More than or equal to 60	More than or equal to 80	More than or equal to 100	More than or equal to 120	More than or equal to 140	More than or equal to 160	More than or equal to 180	More than or equal to 200
Number of Students	90	76	60	55	51	49	33	12	8	4
Draw a ?more than type? ogive and from it, find median. Verify median by actual calculations.

Answer:

Pocket money (in Rs.)	No. of Students	\[c.i.\]	\[{{f}_{i}}\]	\[c{{f}_{i}}\]
More than or equal to 20	90	20 ? 40	14	14
More than or equal to 40	76	40 ? 60	16	30
More than or equal to 60	60	60 ? 80	5	35
More than or equal to 80	55	80 ? 100	4	39
More than or equal to 100	51	100 ? 120	2	41
More than or equal to 120	49	120 ? 140	16	57
More than or equal to 140	33	140 ? 160	21	78
More than or equal to 160	12	160 ? 180	4	82
More than or equal to 180	8	180 ? 200	4	86
More than or equal to 200	4	200 ? 220	4	90
n= 90			90
\[\frac{n}{2}=\frac{90}{2}=45\]
\[\therefore \] Median class is \[120-140\]
Median \[=l+\frac{\frac{n}{2}-cf}{f}\times h\]
\[=120+\frac{45-41}{16}\times 20\]
\[=120+\frac{4\times 20}{16}=120+5=Rs.\,\,125\]                          Hence Verified.