Question

The table below classifies the candidates who took and examination, according to the marks scored by them:

Marks		Number of Candidates
0 − 10 10 − 20 20 − 30 30 − 40 40 − 50 50 − 60 60 − 70 70 − 80 80 − 90 90 − 100		44 40 35 20 12 10 8 6 4 1

Find the median mark.

Answer 1

Given data can be shown as:

Marks		Number of candidate
Below 10		44
Below 20		84
Below 30		119
Below 40		139
Below 50		151
Below 60		161
Below 70		169
Below 80		175
Below 90		179
Below 100		180

Let us tabulate the numbers 10, 20, … in the first row and 44, 84, … in the second row.

x		10		20		30		40		50		60		70		80		90		100
y		44		84		119		139		151		161		169		175		179		180

We know that the change in y is proportional to the corresponding change in x.

We have to find that value of x for which y =

_{The number 90 is between the numbers y = 84 and y = 119.}

_{The corresponding numbers are x = 20 and x = 30.}

_{Thus, we must have:}

Thus, the median marks of the candidates who took an examination is 21.71.