Question

Find the median of the following frequency distribution:

Marks	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
Number of students	6	16	30	9	4

Answer 1

1. Calculate cumulative frequencies

To find the median, we first construct a cumulative frequency table from the given data: 

Marks	Number of students (f)	Cumulative frequency (cf)
0 – 10	6	6
10 – 20	16	6 + 16 = 22
20 – 30	30	22 + 30 = 52
30 – 40	9	52 + 9 = 61
40 – 50	4	61 + 4 = 65

The total number of observations is N = 65.

2. Identify the median class

Next, we calculate the middle position of the data:

`N/2 = 65/2 = 32.5`

The cumulative frequency just greater than or equal to 32.5 is 52, which corresponds to the class interval 20 – 30. Therefore, our median class is 20 – 30.

From this median class, we identify the following components required for the formula:

Lower limit of the median class, L = 20

Frequency of the median class, f = 30

Cumulative frequency of the preceding class, CF = 22

Class width, h = 10

3. Apply the median formula

The formula for the median of a grouped frequency distribution is:

Median = `L + ((N/2 - CF)/f) xx h`

Substitute the values into the formula:

Median = `20 + ((32.5 - 22)/30) xx 10`

Simplify the expression inside the parentheses:

Median = `20 + (10.5/30) xx 10`

Median = `20 + 105/30`

Median = 20 + 3.5

Median = 23.5

The median marks of the students in the given frequency distribution is exactly 23.5.