Q) The marks obtained by 80 students of class X in a mock test of Mathematics are given below in the table. Find median and the mode of the data:

(Q 33 – 30/1/3 – CBSE 2026 Question Paper)

Ans:

Let’s first rearrange the given data in terms of grouped data:

(i) Median value:

Step 1: To calculate the median value, let’s re-organize the data:

To find the median, we need to first identify median class of the data.

• We know that, Median class is the class where the cumulative frequency crosses 50% of total of frequencies.
• Here, in the given data, total of frequencies is 80, hence 50% of it is 40.
• At “50-60” class, cumulative frequency is crossing 40
• Hence, our Median class = 50-60

Step 4: Next, the median value of a grouped data is given by:

Median =

Here:

L = Lower boundary of the median class = 50

n = Total number of frequencies = 80

c_f = Cumulative frequency of the class before the median class = 37

f = Frequency of the median class = 15

h = Class width = 60 – 50 = 10

hence, the Median =

=

=

=

= 50 + 2 = 52

Therefore, the median value is 52 marks.

(i) Modal value:

Let’s look at grouped data again:

Step 3: Since the modal class is the class with the highest frequency.

Here, in th egiven table, highest frequency is 15

∵ highest frequency belongs to class “50 – 60”

∴ the modal class is “50 – 60”.

Step 4: Now mode of the grouped data is calculated by:

Mode =

Here,

L = lower class limit of modal class = 50

f₁ = frequency of modal class = 15

f₀ = frequency of class proceeding to modal class = 12

f₂ = frequency of class succeeding to modal class = 12

h = class size = 60 – 50 = 10

Let’s put values in the formula and solve:

Mode =

=

=

= 50 + = 50 + 5 = 55

Therefore, the modal value is 55 marks.

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