question_answer

From the following data find the median age of 100 residents of a colony who took part in swachch bharat abhiyan:
Age (in yrs.) More than or equal to	No. of residents
0	50
10	46
20	40
30	20
40	10
50	3

Answer:

First convert the given table into C.I. Table.
C.I.	Frequency	c.f.
0 ? 10	4	4
10 ? 20	6	10
20 ? 30	20	30
30 ? 40	10	40
40 ? 50	7	47
50 ? 60	3	50
\[\frac{N}{2}=\frac{50}{2}=25\]
Median \[=l=\left[ h\frac{\left( \frac{N}{2}-c.f. \right)}{f} \right]\]
\[=20+\left[ 10\frac{(25-10)}{20} \right]\]
\[=20+\frac{15}{2}\]
\[=27.5\]