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

Question 13

Step 1: Understand the data.

The table gives us age groups (class intervals) of patients and how many patients are in each group (frequency).

Step 2: Less-than type cumulative frequency.

• For "less than 20": Only the first group (10–20) is included. So CF = 60.
• For "less than 30": Add patients in 10–20 and 20–30 → 60 + 42 = 102.
• For "less than 40": Add one more group → 102 + 55 = 157.
• For "less than 50": Add one more group → 157 + 70 = 227.
• For "less than 60": Add one more group → 227 + 53 = 280.
• For "less than 70": Add the last group → 280 + 20 = 300.

Step 3: More-than type cumulative frequency.

• Start with total patients = 300.
• For "more than or equal to 20": Subtract the first group (10–20) → 300 – 60 = 240.
• For "more than or equal to 30": Subtract next group (20–30) → 240 – 42 = 198.
• For "more than or equal to 40": Subtract next group (30–40) → 198 – 55 = 143.
• For "more than or equal to 50": Subtract next group (40–50) → 143 – 70 = 73.
• For "more than or equal to 60": Subtract next group (50–60) → 73 – 53 = 20.
• For "more than or equal to 70": Subtract last group (60–70) → 20 – 20 = 0.

Step 4: Final tables.

We now have both cumulative frequency distributions as shown above.

This method works by step-by-step addition for "less than type" and subtraction from the total for "more than type".