Question

The frequency distribution has been represented graphically as follows:

Marks	0-20	20-40	40-60	60-100
No. of students	10	15	20	25

Do you think this representation is correct or incorrect?

A. correct
B. incorrect
C. ambiguous
D. data insufficient

Answer 1

Hint: Study the given frequency distribution table of the number of students and the marks scored by them. Then interpret the given graph and write the frequency distribution for it. Then check when it matches with the given data.

Complete step-by-step answer:
According to the table given in the question, the marks are divided into four intervals. The first interval is from 0 marks to 20 marks. The second interval is from 20 marks to 40 marks, the third interval is from 40 marks to 60 marks. The range of the last interval is 40 marks from 60 to 100.
In the second row of the table, the numbers of students that have scored marks from that particular interval are given.
It shows that 10 students have scored marks between 0-20.
15 students have scored marks between 20-40.
20 students have scored marks between 40-60.
25 students have scored marks between 60-100.
In the given graph, the x-axis is representing the marks scored by the students and y-axis is representing the number of students.
The graph is showing that the number of students that scored marks between 0-20 are 10.
The number of students that scored marks between 20-40 are 15.
The number of students that scored marks between 40-60 are 20.
The number of students that scored marks between 60-100 are 12.
And this data matches with the data that we found from the given table.
Therefore, the given graph for the frequency distribution is correct.
So, the correct answer is “Option A”.

Note: Let us calculate the average marks scored by a student.
The class marks of the intervals 0-20, 20-40, 40-60 and 60-100 are 10, 30, 50 and 80.
The average marks scored by a student is equal to the sum of the products of the class mark of an interval and the number of students who scored marks belonging to that interval divided by the total number of students.
The total number of students is $ 10+15+20+25=70 $ .
Therefore, the average marks scored by a student are $ \dfrac{(10)(10)+(30)(15)+(50)(20)+(80)(25)}{70}=\dfrac{3145}{70}=44.92\approx 45marks $ .