Question

Construct the cumulative frequency table for:

Marks	20-29	30-39	40-49	50-59
No. of students	18	23	36	42

Answer 1

Given:

The frequency distribution of marks and the number of students:

• Marks (20-29): 18 students
• Marks (30-39): 23 students
• Marks (40-49): 36 students
• Marks (50-59): 42 students

Formula: Cumulative Frequency of a class = Frequency of the current class + Cumulative Frequency of the preceding class

∴ cf₁ = 18  [Setting the first cumulative frequency equal to the first frequency]

∴ cf₂ = 18 + 23 = 41  [Adding the second frequency to the previous cumulative frequency]

∴ cf₃ = 41 + 36 = 77  [Adding the third frequency to the previous cumulative frequency]

∴ cf₄ = 77 + 42 = 119  [Adding the fourth frequency to the previous cumulative frequency]

The cumulative frequency table is as follows:

Marks	No. of students	Cumulative Frequency
20 - 29	18	18
30 - 39	23	41
40 - 49	36	77
50 - 59	42	119

∴ The cumulative frequencies are 18, 41, 77, and 119 respectively.