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Question
Construct the class boundaries and less than cumulative frequency table for the given frequency distribution table. Also construct a less than frequency curve for the given data.
Class IntervalFrequency1−3104−6127−91510−121313−159
Class IntervalFrequency1−3104−6127−91510−121313−159
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Solution
The given frequency distribution is in the inclusive form. First, we convert it into exclusive form.
Now, consider the classes 1-3, 4-6.
The lower limit of 4-6 is 4.
The upper limit of 1-3 is 3.
Thus, the half of the difference is 4−32=12=0.5
So, we subtract 0.5 from each lower limit and add 0.5 to each upper limit.
The table for continuous grouped frequency distribution is given below.
Class IntervalFrequencyClass BoundaryUpper BoundaryLess than CF1−3100.5−3.53.5104−6123.5−6.56.5227−9156.5−9.59.53710−12139.5−12.512.55013−15912.5−15.515.559
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.
Now, consider the classes 1-3, 4-6.
The lower limit of 4-6 is 4.
The upper limit of 1-3 is 3.
Thus, the half of the difference is 4−32=12=0.5
So, we subtract 0.5 from each lower limit and add 0.5 to each upper limit.
The table for continuous grouped frequency distribution is given below.
Class IntervalFrequencyClass BoundaryUpper BoundaryLess than CF1−3100.5−3.53.5104−6123.5−6.56.5227−9156.5−9.59.53710−12139.5−12.512.55013−15912.5−15.515.559
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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