012. Cumulative Frequency Distributions

Determination of the number of observations that are greater than or less than some amount can be done through the use of a Less-than cumulative frequency distribution or a More-than cumulative frequency distribution. Cumulative frequency tables can easily be constructed from their respective frequency tables.

A Less-than cumulative frequency Distribution For a particular class is found by adding the frequency in that class to those in all previous classes. Table 2.6 shows a less-than cumulative frequency distribution for the data set on passengers. The frequencies from Table 2.3 are repeated in Table 2.6. It can be seen that, on 40 of the 50 days, less than 90 passengers flew the airways of P&P.

Table 2.6 – Less-Than Cumulative Frequency Distribution for the Number of Passengers

Class (passengers)	Frequency (days)	Cumulative Frequency (days)
Less than 50	0	0
Less than 60	3	3
Less than 70	7	10
Less than 80	18	28
Less than 90	12	40
Less than 100	8	48
Less than 110	2	50

For a more-than cumulative frequency distribution, the values are found by subtracting frequencies of previous classes. This is reflected in Table 2.7. using Table 2.3 it can be found that on all 50 days at least 50 passengers boarded P&P Airlines. Since less that 60 passengers bought tickets only on three of the 50 days, then on remaining 47 days, 60 or more people flew P&P, on 22 days at least 80 passengers flew the airline.

Table 2.7 – More - Than Cumulative Frequency Distribution for the Number of Passengers

Class (passengers)	Frequency (days)	Cumulative Frequency (days)
50 or more	3	50
60 or more	7	47
70 or more	18	40
80 or more	12	22
90 or more	8	10
100 or more	2	2
110 or more	0	0

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