Consider the grouped frequency distribution of several tenders received by a department from the contractors for civil work in a course of time. Construct the less than cumulative frequency table and the respective ogive.

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Solution

For drawing the less than cumulative frequency table and the respective ogive first we have to calculate the upper boundary and less than CF.

In class interval 0-4, upper boundary is 4. Similarly we will calculate other upper boundaries.

For calculating less than CF we will keep adding successively the frequencies of all the previous classes along with the class against which it is written. For example less than CF of class intervals 4-8 is 2+5=7. Similarly we will calculate the others less than CF.

Below given table consist of upper boundary as well as less than CF.

Now we will draw the less than frequency curve by taking upper boundary on X-axis and less than CF on Y-axis with suitable scale.

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Similar questions

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

Marks	1 - 10	11 - 20	21 - 30	31 - 40	41 - 50	51 - 60	61 - 70	71 - 80
Frequency	3	8	12	14	10	6	5	2

\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	$6$	$14$	$20$	$21$	$9$	$5$

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