draw a less than ogive from the following data and hence find out the value of median: age 0-10 10-2020-30 30-40 40-5050-60 60-70 70-80 number 10 15 22 16 14 12 6 5

cc,

To construct a less than ogive, ​we first need to convert the series into a less than cumulative frequency distribution.
 

Age	Number(f)	Cumulative frequency(c.f)
Less than 10	10	10
Less than 20	15	25
Less than 30	22	47
Less than 40	16	63
Less than 50	14	77
Less than 60	12	89
Less than 70	6	95
Less than 80	5	100

Median class is given by the size of the ${\left(\frac{N}{2}\right)}^{th}$ item, i.e. the ${\left(\frac{100}{2}\right)}^{th}$item, which is the 50th item.
This corresponds to the class interval 30−40, so this is the median class.

$$\begin{gathered} \mathrm{Median}\left(M\right) =l_{1 }+ \frac{ {\displaystyle \frac{N}{2}} - cf}{f} \times i \\ =30 +\frac{ {\displaystyle \frac{100}{2}} - 47}{16} \times 10 \\ =30 + \frac{ 30}{16} \\ M = 31.88 \end{gathered}$$