Construct class intervals and frequencies for the following distribution table. Also draw the less than cumulative frequency curve for the same.

[5 marks]

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Solution

The required table is given below:

[2.5 marks]

Less than cumulative frequency curve:

Step 1: Mark the upper boundaries of the class intervals along X -axis and their corresponding cumulative frequencies along Y- axis.

Select the scale : X-axis 1 smallest unit = 1 mark
Y-axis 1 smallest unit = 0.8 students

Step 2: Also, plot the lower boundary of the first class (upper boundary of the class previous to first class) interval with cumulative frequency 0.

Step 3: Join these points by a free hand curve to obtain the required curve.

[2.5 marks]

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Mark	Cumulative Frequency
Less than 5 Less than 15 Less than 25 Less than 35 Less than 45 Less than 55 Less than 65 Less than 75	0 3 5 15 44 70 91 106

\begin{matrix} Class Interval & Frequency 1 - 3 & 10 4 - 6 & 12 7 - 9 & 15 10 - 12 & 13 13 - 15 & 9 \end{matrix}

Class Marks	$10$	$22$	$34$	$46$	$58$	$70$
Frequency	$6$	$14$	$20$	$21$	$9$	$5$

Marks obtained	Less than $5$	Less than $10$	Less than $15$	Less than $20$	Less than $25$
No of students	$2$	$8$	$18$	$27$	$35$

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