Question

The following distribution of ages (in complete years) is obtained for the students of higher secondary. The median of the distribution is

Age (in years)	15	16	17	18	19	20	21
Number of students	12	18	20	10	7	6	2

Answer 1

Hint: In the given table, frequency is the row of “Number of students”. Add one more column in the given table as “cumulative frequency”. To calculate the cumulative frequency of each row, add the entries in the frequency column up to that row. Now, calculate the middle number of the entry at the bottom of the cumulative frequency column. Then, get the row in which the middle number falls and conclude the median.

Complete step-by-step solution:
According to the question, we have the distribution of ages (in complete years) for the students of higher secondary.
In the given table, frequency is the row of “Number of students”.
First of all, we need to modify the given table.
Let us add one more column in the given table as “cumulative frequency”.
For calculating the cumulative frequency of each row, we have to add the entries in the frequency column up to that row.
Now, on modifying the given table, we get

Age (in years)	Number of students	Cumulative frequency
15	12	12
16	18	12+18=30
17	20	12+18+20=50
18	10	12+18+20+10=60
19	7	12+18+20+10+7=67
20	6	12+18+20+10+7+6=73
21	2	12+18+20+10+7+6+2=75

In the modified table, we have the 75 as our entry at the bottom of the cumulative frequency column.
Now, on calculating the middle number of 75, we get
The middle number = \[\dfrac{75}{2}=37.5\]
Here, we have to find the entry in the cumulative frequency column where our middle number 37.5, falls.
After observing the modified table, we can see that our middle number 37.5, falls in the third row.
Therefore, the median of the given distribution table is 17.

Note: Take into consideration that the median is the middle number in a sorted list of numbers which can be in either ascending or descending order. For instance, if there are 5 numbers sorted in ascending order, then the median of these numbers is the third number.