question_answer

The table below shows the salaries of 280 persons:
Salary (In thousand Rs.)	No. of Persons
5 ? 10	49
10 ? 15	133
15 ? 20	63
20 ? 25	15
25 ? 30	6
30 ? 35	7
35 ? 40	4
40 ? 45	2
45 ? 50	1
Calculate the median salary of the data.

Answer:

Salary	No. of Persons	Cumulative frequency (c.f.)
5 ? 10	49
		182
15 ? 20	63	245
20 ? 25	15	260
25 ? 30	6	266
30 ? 35	7	273
35 ? 40	4	277
40 ? 45	2	279
45 ? 50	1	280
Total	280
\[\frac{N}{2}=\frac{280}{2}=140\]
The cumulative frequency just greater than 140 is 182.
\[\therefore \] Median class is 10 ? 15.
\[\Rightarrow \]\[l=10,h=5,N=280,\,c.f=49\,\] and \[f=133\]
Median \[=1+\left( \frac{\frac{N}{2}-c.f.}{f} \right)\times h\]
\[=10+\left( \frac{140-49}{133} \right)\times 5\]
\[=10+\frac{91\times 5}{133}\]
\[=10+\frac{455}{133}\]
\[=10+3.42\]
\[=13.42\]