## Introduction to Data Interpretation

#### Data Interpretation

Direction: In each of the following questions, the following histogram shows the relationship between the marks obtained by the students and the number of students in an examination. Study the histogram and answer the questions.

1. The ratio of the number of students who obtained 60 or more marks to that of students who obtained 60 or less marks is

1. As per the given above histogram , we can see
Total number of students who obtained 60 or more marks = 19 + 13 = 32
Total number of students who obtained 60 or less marks = 5 + 10 + 15 = 30
Required ratio = Total number of students who obtained 60 or more marks : Total number of students who obtained 60 or less marks

##### Correct Option: D

As per the given above histogram , we can see
Total number of students who obtained 60 or more marks = 19 + 13 = 32
Total number of students who obtained 60 or less marks = 5 + 10 + 15 = 30
Required ratio = Total number of students who obtained 60 or more marks : Total number of students who obtained 60 or less marks
∴ Required ratio = 32 : 30 = 16 : 15

1. The percentage of students who obtained 40 marks or less is

1. On the basis of given graph in question ,
Total number of students = 5 + 10 + 15 + 19 + 13 = 62
Number of students who obtained 40 marks or less = 15

 Required percent = Number of students who obtained 40 marks or less × 100 % Total number of students

##### Correct Option: C

On the basis of given graph in question ,
Total number of students = 5 + 10 + 15 + 19 + 13 = 62
Number of students who obtained 40 marks or less = 15

 Required percent = Number of students who obtained 40 marks or less × 100 % Total number of students

 Required percent = 15 × 100 ≈ 24.2% 62

Direction: Study the histogram of marks (in Mathematics) distribution of 50 students of class IX and answer the following questions.

1. The percentage of students who have secured marks more than 59 is:

1. According to given graph, we have
Students who score more than 59 marks = 4 + 13 = 17
Total number of students = 7 + 8 + 18 + 4 + 13 = 50

 ∴ Required percent = Students who score more than 59 marks × 100 % Total number of students

##### Correct Option: C

According to given graph, we have
Students who score more than 59 marks = 4 + 13 = 17
Total number of students = 7 + 8 + 18 + 4 + 13 = 50

 ∴ Required percent = Students who score more than 59 marks × 100 % Total number of students

 ∴ Required percent = 17 × 100 = 34% 50

1. The number of students who have scored between 39 and 80 is :

1. From the given above histogram , we can see
The number of students who have scored interval 40-60 = 18
The number of students who have scored interval 60-80 = 4
Required answer = The number of students who have scored interval 40-60 + The number of students who have scored interval 60-80

##### Correct Option: A

From the given above histogram , we can see
The number of students who have scored interval 40-60 = 18
The number of students who have scored interval 60-80 = 4
Required answer = The number of students who have scored interval 40-60 + The number of students who have scored interval 60-80
∴ Required answer = 18 + 4 = 22

1. The average marks of the students are

1. On the basis of given graph in question , we have
Here , f1 = 10 , x1 = 7 , f2 = 30 , x2 = 8 , f3 = 50 , x3 = 18 , f4 = 70 , x4 = 4 , f5 = 90 , x5 = 13

 Mid-value of class-interval (x) = Highest value + Lowest value 2

 ∴ Average = Σ fx Σ f

where Σf = Total number of students
 Required average marks = 10 × 7 + 30 × 8 + 50 × 18 + 70 × 4 + 90 × 13 50

##### Correct Option: A

On the basis of given graph in question , we have
Here , f1 = 10 , x1 = 7 , f2 = 30 , x2 = 8 , f3 = 50 , x3 = 18 , f4 = 70 , x4 = 4 , f5 = 90 , x5 = 13

 Mid-value of class-interval (x) = Highest value + Lowest value 2

 ∴ Average = Σ fx Σ f

where Σf = Total number of students
 Required average marks = 10 × 7 + 30 × 8 + 50 × 18 + 70 × 4 + 90 × 13 50

 Required average marks = 70 + 240 + 900 + 280 + 1170 50

 Required average marks = 2660 = 53.2 50