Question

The marks obtained by 40 students of a class in an examination are given below. Present the data in the form of a frequency distribution using equal class-size, one such class being 10 – 15 (15 not included).

15, 23, 6, 23, 8, 17, 16, 8, 16, 10, 7, 5, 2, 18, 7, 12, 10, 3, 20, 3, 20, 13, 1, 21, 13, 3, 23, 16, 13, 18, 12, 5, 24, 9, 2, 7, 18, 23, 4, 12

Answer 1

Given: Data: 15, 23, 6, 23, 8, 17, 16, 8, 16, 10, 7, 5, 2, 18, 7, 12, 10, 3, 20, 3, 20, 13, 1, 21, 13, 3, 23, 16, 13, 18, 12, 5, 24, 9, 2, 7, 18, 23, 4, 12 (40 marks). One class is 10 – 15 (15 not included), so class-size = 5; use equal classes covering the range 1 – 24.

Step-wise calculation:

1. Find range and classes:

Minimum = 1, Maximum = 24 classes of width 5 that cover the data:

0 – 5, 5 – 10, 10 – 15, 15 – 20, 20 – 25 (upper limit not included for each class)

2. Tally/count observations in each class:

0 – 5 (0 ≤ x < 5): 

Values = 1, 2, 2, 3, 3, 3, 4

Frequency = 7

5 – 10 (5 ≤ x < 10):

Values = 5, 5, 6, 7, 7, 7, 8, 8, 9

Frequency = 9

10 – 15 (10 ≤ x < 15):

Values = 10, 10, 12, 12, 12, 13, 13, 13

Frequency = 8

15 – 20 (15 ≤ x < 20):

Values = 15, 16, 16, 16, 17, 18, 18, 18

Frequency = 8

20 – 25 (20 ≤ x < 25):

Values = 20, 20, 21, 23, 23, 23, 23, 24

Frequency = 8

3. Check: 7 + 9 + 8 + 8 + 8 = 40 (matches total observations).

Frequency distribution (class intervals with frequency):

Class	Number of students
0 – 5	7
5 – 10	9
10 – 15	8
15 – 20	8
20 – 25	8
Total	40