1.

Obtain an inclusive continuous frequency distribution from the following data:

Answer»

Given data is ‘more than’ type cumulative frequency distribution.
∴ Class length = Difference between the adjoining lower boundary points = 54.5 – 49.5 = 5
Now, upper boundary point of the class = lower boundary point + class length
For initial class lower boundary point = 44.5
∴ initial class is 44.5 – 49.5.

For inclusive continuous frequency distribution lower limit of initial class = 44.5 + 0.5 = 45 and upper limit of initial class = 49.5 – 0.5 = 49.
Thus, for given data the initial class in inclusive form, we get 45-49.
In this manner, we will obtain the class for each lower boundary point.
We will find the frequency of each class from the given ‘more than’ cumulative frequency as follows :

Frequency of a class = (‘more than’ cumulative frequency of a class) – (‘more than cumulative frequency of immediate following class)

Frequency of class for 44.5 = (‘more than’ cumulative frequency of a class for 44.5) – (‘more than cumulative frequency of immediate following class for 49.5)
= (500 – 470) = 30

In this manner we will obtain the frequency for the rest of classes.
For the given data, we get the inclusive continuous frequency distribution as follows :

Lower Boundary point or moreMore than’ cumulative frequency CfClassFrequency f
44.550045-49500 – 470 = 30
49.547050-54470 – 390 = 80
54.539055-59           .390 – 290 = 100
59.529060-64290 – 240 = 50
64.524065-69240 – 90 = 150
69.59070-7490 – 10 = 80
74.51075-7910 – 0 = 10
79.5080-84= 0
Totaln = 500


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