Question

Marks of high school students are distributed in the table given below.

Marks (Class marks)	2.5	7.5	12.5	17.5	22.5
No. of Students (Frequency)	16	20	12	6	8

Build a histogram and find out the number of students having marks at least 15.

• A.
• B. 8 students have at least 15 marks.
• C.
• D. 14 students have at least 15 marks.

Answer 1

Answer: (A), (D)

The correct options are
A
D 14 students have at least 15 marks.

We have to first calculate the class interval from the class marks.

Difference between the two successive classes = h = 7.5 - 2.5 =5.

If x is the class marks then, lower and upper boundary of every class is x - $\frac{h}{2}$ and x + $\frac{h}{2}$.

Class marks (Marks)	Frequency (No. of students)	Class intervals
2.5	16	0 - 5
7.5	20	5 - 10
12.5	12	10 - 15
17.5	6	15 - 20
22.5	8	20 - 25

Take suitable scale ,
On X-axis 1 cm = 1 class interval
On Y-axis 1 cm = 4 students

Take class intervals on X-axis and frequency on Y-axis.

Now plot the bar in the graph with respect to the class interval.

Students having marks at least 15 is the sum of the frequency of class 15 - 20 and 20 - 25 = 6 + 8 = 14.