NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3
Question 14

Question. 14

14. Given cumulative (less-than) marks of 50 students:

Marks	Below 20	Below 40	Below 60	Below 80	Below 100
No. of students	17	22	29	37	50

Form the ordinary frequency distribution.

Class	0–20	20–40	40–60	60–80	80–100
Frequency	17	5	7	8	13

Step 1: Understand what the given table means.

The numbers given are cumulative frequencies. For example, "Below 40 = 22" means 22 students scored less than 40 marks.

Step 2: Write the class intervals.

The marks are given in groups of 20. So the classes will be: 0–20, 20–40, 40–60, 60–80, 80–100.

Step 3: Find the frequency for each class.

For 0–20: Directly take "Below 20" = 17.
For 20–40: Subtract "Below 20" from "Below 40". \(22 - 17 = 5\).
For 40–60: Subtract "Below 40" from "Below 60". \(29 - 22 = 7\).
For 60–80: Subtract "Below 60" from "Below 80". \(37 - 29 = 8\).
For 80–100: Subtract "Below 80" from "Below 100". \(50 - 37 = 13\).

Step 4: Write the ordinary frequency table.

Class	0–20	20–40	40–60	60–80	80–100
Frequency	17	5	7	8	13

Final Answer: The ordinary frequency distribution is as shown above.