Question

Compute the median for each of the following data:

(i)

Marks	No. of students
Less than 10 Less than 30 Less than 50 Less than 70 Less than 90 Less than 110 Less than 130 Less than 150	0 10 25 43 65 87 96 100

(ii)

Marks	No. of students
More than 150 More than 140 More than 130 More than 120 More than 110 More than 100 More than 90 More than 80	0 12 27 60 105 124 141 150

Answer 1

(i)

We prepare the cumulative frequency table, as given below.

Now, we have

So,

Now, the cumulative frequency just greater than 50 is 65 and the corresponding class is .

Therefore, is the median class.

Here,

We know that

Hence, the median is 76.36.

Note: The first class in the table can be omitted also.

(ii)

We prepare the cumulative frequency table, as given below.

Now, we have

So.

Thus, the cumulative frequency just greater than 75 is 105 and the corresponding class is .

Therefore, is the median class.

(Because class interval given in descending order)

We know that

= 120 − 3.333

= 116.67 (approx)

Hence, the median is 116.67.