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 |