Question
Download Solution PDFStudy 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:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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.
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