Frequency Distributions and Cumulative Frequency Distributions

Statistics By Safi Ur Rehman Qamar November 23, 2024 No Comments

Frequency Distributions (FD)

When the class intervals (in terms of class boundaries, limits, or marks) are displayed in tabular form along with the corresponding class frequencies, the resulting table is known as a frequency distribution.

The classes in the table below are given in terms of their class limits. Since we have already arranged the data in order, counting the number in each class can be done very quickly. The frequency distribution for the SAT-Verbal data is shown in Table 1.

Table 1

Class	Gass limits	Class frequency
1	425—449	1
2	450-474	2
3	475-499	5
4	5tO-524	6
5	525—549	20
6	550—574	7
7	575-599	15
8	61Xt—624	16
9	625—649	11
10	650—674	9
11	675—699	4
12	700-724	2
13	725—749	2

Example

If the data are not arranged in order, then probably the quickest way to classify them is to read down the list of the unordered data, placing a tally mark opposite the appropriate class for each observation. Then the tallies are totalled and the class frequencies written. The first three observations are 546, 689, and 490; so, as we read down the list of unclassified data, we would place a tally opposite the fifth (525-549), eleventh (675-699), and third (475- 499) classes, in that order. Proceeding in like manner until we have a tally for each observation, then totalling the tally marks to obtain the class fre- quencies, we obtain Table 2.

Table 2

Class

Class Class limits Tallies frequency

1 425—449 | 1

2 450-474 | | 2

3 475—499 5

4 500—524 | 6

5 525—549 20 Frequency

6 550-574 | ] 7

7 575-599 15

8 600—624 | 16

9 625—649 | 11

10 650—674 | | ] | 9

11 675-699 I 1 1 1 4

12 700—724 | | 2

13 725-749 1 1

Cumulative FD

The cumulative frequency distribution is a table showing the number of observations that are less than specified values. It is convenient to use the lower class limits (beginning with the second class) for the specified values. When this is done the cumulative frequencies become the frequency of the first class, sum of the frequencies of the first two classes, and so on.

The cumulative frequency distribution for the SAT-Verbal data is shown in Table 3.

Table 3 Cumulative Frequency Distributation

Less than	450	1
Lessthan	475	3
Less than	500	8
Less than	525	14
Lessthan	550	34 Frequency
Less than	575	41
Less than	600	56
Less than	625	72
Less than	650	83
Less than	675	92
Less than	700	96
Less than	725	98
Less than	750	100 Frequency