We will start by looking at a graphical method for studying the variation known as the 'Frequency Histogram'.
To create a frequency histogram, group the data into bins, each bin containing a range of values. The data below show the test results for 25 students:
Results


Bin

Frequency

38

10

60

90

88


>020

7

96

1

41

86

14


>2040

8

25

5

3

16

22


>4060

5

2

29

34

55

36


>6080

0

37

36

91

47

43


>80100

5

I've grouped them into 5 bins of equal span. The first bin contains the frequency (or number) of results that are greater than zero and up to and including 20. The second bin contains the frequency of values greater than 20 up to and including 40. I've shaded these values to make it easier for you to check that there are eight (38, 25, 37, 29, 36, 34, 22 and 36).
Now I can create a histogram of the results. The vertical axis represents the frequency of observations in each range:

Note that you can count the frequencies as you create the histogram. As you read the data values put a cross in the appropriate bin on the histogram.
Roll your mouse over the image to see this.
