FREQUENCY DISTRIBUTION

Frequency Distribution or Organizing the Data
Lecture 2

After the collecting stage, the data must be organized. A frequency distribution table or polygon can be used to:
1- Summarize and compressing data by grouping it into classes and recording how many data points occurs into each class.
2. Present the data and produce a “snapshot” of it.
3. Compute of various statistical measures.

There are two types of frequency distributions:
1- Ungrouped (or simple) frequency distributions used for:
a- Qualitative variables (nominal and ordinal).
b- Discrete quantitative variables with a few different values.
2- Grouped frequency distributions used for:
a- Continuous quantitative variables.
b- Discrete quantitative variables with large number of different values (more than 20).

1. Ungrouped or simple frequency distribution

Example:
The following data represent the number of children of 16 Iraqi women:

3, 5, 2, 4, 0, 1, 3, 5, 2, 3, 2, 3, 3, 2, 4, 1
Solution:
Use the following steps to present this data in a frequency distribution table:
1- Variable: In this data the type of variable is discrete quantitative variable with a few different values (n=16), so we must arrange in ungrouped frequency distribution.
2- Divide the data into intervals or types of elements (X), the possible values of the variable are: 0, 1, 2, 3, 4, 5, and then count the number of data in each interval or number of each element (F).
3- Create a table with four columns.
- In the first column you would put the intervals of the data.
- Next column is the frequency column (No. of women for each interval).
- The third column is the relative frequency column, find out by:

…………………… (n=sample size)

- The final column is the percentage frequency column.




Simple frequency distribution of the No. of children of Iraqi women

No. of children
(X) No. of women
(F) Relative Frequency
(R.F.= F/n) Percentage Freq.
(R.F.%=R.F.×100)
0 1 0.0625 6.25%
1 2 0.125 12.5%
2 4 0.25 25%
3 5 0.312 31.25%
4 2 0.125 12.5%
5 2 0.125 12.5%
Total n=16 1.00 100%



Frequency bar chart is a graphical representation for the simple frequency distribution


2. Grouped frequency distribution

Example:
The following are the hemoglobin values (g/dl) of 30 children receiving treatment for hemolytic anemia.

10.0 8.7 6.7 7.8 8.9 10.8
9.7 9.9 8.5 7.5 9.0 10.0
9.1 9.1 8.4 10.6 10.2 8.5
8.6 9.7 9.7 9.6 10.2 11.4
12.2 9.4 9.3 8.4 8.2 9.2

Solution:
Use the following steps to present this data in a frequency distribution table:
1- Variable: In this data the type of variable is continuous quantitative with large number of different values (n=30), so we must arrange in grouped frequency distribution.

2- Classes: To summarize data into classes, the approximate number of classes can be determined by this formula:
No. of classes = 1+ 3.322 (Log10 n)
= 1+ 3.322 (Log10 30) ? 6
Or this formula:
No. of classes ? 6

3- Class interval: is the different between the lowest and highest possible values in each class. And to compute it finds the different between the highest and lowest value of the data, and divide on number of classes.

Class interval ? 1


4- To arrange the data into classes as follow:
- First class lower value = lowest values of the data………….……. (Approximately)
Upper value = first lower value + Class interval
- Second class lower value = Upper value for first class
Upper value = lower value + Class interval ……………..…………. (etc)