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

Question 5

Step 1: Write the class intervals and their frequencies (f).

Step 2: Find the class marks (mid-points).

Formula: \(x = \dfrac{\text{lower limit} + \text{upper limit}}{2}\)

• For 1–200: \(x = \dfrac{1 + 200}{2} = 100.5\)
• For 201–400: \(x = \dfrac{201 + 400}{2} = 300.5\)
• For 401–600: \(x = \dfrac{401 + 600}{2} = 500.5\)
• For 601–800: \(x = \dfrac{601 + 800}{2} = 700.5\)

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

Step 4: Find totals.

• \(\sum f = 14 + 15 + 14 + 7 = 50\)
• \(\sum (f × x) = 17825\)

Step 5: Apply the formula for Mean.

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

\(\bar{x} = \dfrac{17825}{50} = 356.5\)

Final Answer: Mean daily income = Rs 356.5