Study the given histogram and answer the questions that follow.

The histogram shows the distribution of marks obtained by 115 students in a college.

A student is marked as qualified if he/she obtains marks above 40.5. Here, the ratio of the number of qualified students to that of students who are not qualified is:

Question

Question

This question was previously asked in

SSC CHSL Exam 2024 Tier-I Official Paper (Held On: 08 Jul, 2024 Shift 4)

Answer 1

Given:

Total number of students = 115

Frequency densities and intervals:

Marks 20.5 to 30.5: Frequency density ≈ 0.5

Marks 30.5 to 40.5: Frequency density ≈ 1.5

Marks 40.5 to 50.5: Frequency density ≈ 2.5

Marks 50.5 to 60.5: Frequency density ≈ 3.0

Marks 60.5 to 70.5: Frequency density ≈ 2.0

Marks 70.5 to 80.5: Frequency density ≈ 1.0

Marks 80.5 to 90.5: Frequency density ≈ 1.0

Formula used:

Frequency = Frequency density × Width of the bar

Qualified students: Marks > 40.5

Non-qualified students: Marks ≤ 40.5

Calculation:

Step 1: Calculate the number of qualified students (marks above 40.5)

Marks 40.5 to 50.5: Frequency = 2.5 × 10 = 25

Marks 50.5 to 60.5: Frequency = 3.0 × 10 = 30

Marks 60.5 to 70.5: Frequency = 2.0 × 10 = 20

Marks 70.5 to 80.5: Frequency = 1.0 × 10 = 10

Marks 80.5 to 90.5: Frequency = 1.0 × 10 = 10

Total number of qualified students = 25 + 30 + 20 + 10 + 10 = 95

Step 2: Calculate the number of non-qualified students (marks ≤ 40.5)

Marks 20.5 to 30.5: Frequency = 0.5 × 10 = 5

Marks 30.5 to 40.5: Frequency = 1.5 × 10 = 15

Total number of non-qualified students = 5 + 15 = 20

Step 3: Calculate the ratio of qualified to non-qualified students

⇒ Ratio = Number of qualified students / Number of non-qualified students

⇒ Ratio = 95 / 20

⇒ Ratio = 19 : 4

∴ The ratio of the number of qualified students to the number of non-qualified students is 19 : 4.