NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3

Question 2

Step 1: Write down the class intervals and frequencies.

We are given:

• Marks (class intervals): 10–20, 20–30, 30–40, 40–50, 50–60
• Number of students (frequency, f): 2, 4, 7, 6, 1

Step 2: Find the class marks (x).

Class mark = (lower limit + upper limit) ÷ 2

• For 10–20: (10 + 20) ÷ 2 = 15
• For 20–30: (20 + 30) ÷ 2 = 25
• For 30–40: (30 + 40) ÷ 2 = 35
• For 40–50: (40 + 50) ÷ 2 = 45
• For 50–60: (50 + 60) ÷ 2 = 55

So, class marks are: 15, 25, 35, 45, 55.

Step 3: Multiply frequency (f) with class mark (x).

Step 4: Add the totals.

• Total of frequencies, \(\sum f = 2 + 4 + 7 + 6 + 1 = 20\)
• Total of f × x, \(\sum f x = 30 + 100 + 245 + 270 + 55 = 700\)

Step 5: Apply the formula of mean.

Mean, \(\bar{x} = \dfrac{\sum f x}{\sum f}\)

\(\bar{x} = \dfrac{700}{20} = 35\)

Final Answer: The mean marks = 35.