# Cumulative Frequency Distribution

The total frequency of all classes less than the upper class boundary of a given class is called the cumulative frequency of that class. A table showing the cumulative frequencies is called a cumulative frequency distribution. There are two types of cumulative frequency distributions.

Less than cumulative frequency distribution:

It is obtained by adding successively the frequencies of all the previous classes including the class against which it is written. The cumulate is started from the lowest to the highest size.

More than cumulative frequency distribution:

It is obtained by finding the cumulate total of frequencies starting from the highest to the lowest class. The less than cumulative frequency distribution and more than cumulative frequency distribution for the frequency distribution are given below:

 Less than C.F More than C.F Class Limit $f$ Class  Boundaries Marks C.F Marks C.F 10 - 19 2 9.5 – 19.5 Less than 19.5 2 9.5 or more 48 + 2 = 50 20 - 29 4 19.5 – 39.5 Less than 29.5 2 + 4 = 6 19.5 or more 44 + 4 = 48 30 - 39 7 29.5 – 39.5 Less than 39.5 6 + 7 = 13 29.5 or more 37 + 7 = 44 40 - 49 10 39.5 – 49.5 Less than 49.5 13 + 10 = 23 39.5 or more 27 + 10 = 37 50 - 59 16 49.5 – 59.5 Less than 59.5 23 + 16 = 39 49.5 or more 11 + 16 = 27 60 - 69 8 59.5 – 69.5 Less than 69.5 39 + 8 = 47 59.5 or more 3 + 8 = 11 70 - 79 3 69.5 – 79.5 Less than 79.5 47 + 3 = 50 69.5 or more 3 50