In annual day of a school, age-wise participation of students is shown in the following frequency distribution:
Age of students (in years) 5-7 7-9 9-11 11-13 13-15 15-17 17-19
Number of students 20 18 22 25 20 15 10
Draw a ‘less than type’ ogive for the above data and from it find the median age.

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Detailed Solution

We are given data, and we have to form a less than type ogive and find the median. The less-than-type table can be written as

Age (class)	Number of Students (frequency)
Less than 7	20
Less than 9	38
Less than 11	60
Less than 13	85
Less than 15	105
Less than 17	120
Less than 19	130
The ogive is shown below:

The 𝑥 − 𝑎𝑥𝑖𝑠 is taken as the age of students, and the 𝑦 − 𝑎𝑥𝑖𝑠 is taken as the number of students

This table shows that the total frequency, or the total number of students, is 130. So, the middlemost age student = 130/2
= 65
In the graph, the 𝑥 − 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒 corresponding to the 𝑦 − 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒 of 65 is 11. 4. Hence, the median age is 11. 4 years.