Less Than Cummulative Frequecy Distribution


 
 
Concept Explanation
 

Less Than Cumulative Frequency Table

-Cumulative frequency curve or an ogive is the graphical representation of a cumulative frequency distribution. There are two methods of constructing an ogive

(i) Less than method                            (ii) More than method

 (i) Less than method : - Following are the steps for construction of an ogive :

(a) Construct a cumulative frequency table of less than type.

(b) Mark upper class limits along X-axis.

(c) Mark the corresponding cumulative frequency along Y-axis.

(d) Plot the points (x_i, f_i), where x_i is the upper limit of a class and f_i is the corresponding c.f. and join them by a smooth free hand curve.

The curve we get is the Less Than Type Ogive.

Illustration : - Draw an ogive for the following frequency distribution by less than method.

Class Interval 0-8 8-16 16-24 24-32 32-40 40-48
Frequency 8 12 20 16 8 10

Solution : First we prepare a Less Than Type frequency distribution table.

Class Interval Cumulative Frequency
Less than 8 8
Less than 16 8+12=20
Less than 24 20+20=40
Less than 32 40+16=56
Less than 40 56+8=64
Less than 48 64+10=74

Now, mark the upper class limit on X-axis and frequency along Y-axis, plot the point (8,8), (16,20), (24,40), (32,56), (40,64) and (48,74). Join the points by smooth free hand curve to get required less than type ogive.

 

 
 


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