Find the mean, mode and median of marks obtained by 20 students in an examination.

The marks are given below.

We have

For Mean:

Mean is given by

⇒ [from the table]

⇒ Mean = 28

For Median:

Here, we get total frequency, ∑f_i = N = 20. So,

Since, N/2 = 10. Mark a cumulative frequency which is just greater than 10.

Here, it is 18. So, median class would be 30 – 40.

Median is given by

Where, l = lower limit of the median class = 30

N/2 = 10 (as calculated above)

m = cumulative frequency of the class preceding the median class = 10

f = frequency of the median class = 8

c = width of the median class = 10

Putting all these values in the formula, we get

⇒

⇒ Median = 30 + 0 = 30

For Mode:

We have the following data in exclusive type in tabular form. We can interpret the column ‘No. of students’ as frequency.

Note that, highest frequency = 8

Corresponding class interval = 30 – 40

⇒ Modal class = 30 – 40

Mode is given by,

Where, l = lower limit of the modal class = 30

f = frequency of the modal class = 8

f₁ = frequency of the class preceding the modal class = 5

f₂ = frequency of the class succeeding the modal class = 2

c = width of the class interval = 10

Putting all these values in the modal formula,

⇒

⇒

⇒ Mode = 30 + 3.33

⇒ Mode = 33.3

Thus, mean is 28, median is 30 and mode is 33.3.