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# How do you construct a cumulative relative frequency distribution?

Definitionwise cumulative frequency are simply accumulated frequency.

Let's have the following definition:

Less than cumulative frequency (<Cf) is the number of observations less than the upper class boundary of a class.

Greater than cumulative frequency (>Cf) is the number of observations greater than the lower class boundary of a class.

Let's take this example

The first entry at <Cf simply the number of observations less than 3.5 since the maximum score of that class is 3 (1 - 3)

The next entry is 6 since the number of observations less than 6.5 is the combined frequency of the class 1 - 3 and 4 - 6. 2 + 4 = 6 and do the same process.. 11 is taken by 2 + 4 + 5 = 11 and so on..

Same concept to be applied for >Cf but this time that is number of observations greater than the lower class boundary of a class. The first entry is 20.. intuitively since the lowest score is one, meaning all the observations is greater than 0.5. How many observations are less than 3.5? the answer is 20 - 2 = 18 which is the second entry, because there are tow observations that are not greater than 3.5 those scores ranges from 1 - 3.