A frequency distribution table can be created using the frequency table creation process and the raw quantitative data shown below. Step 1:

Choose 6 for the number of classes.

Step 2: Use the class width formula to find the class width.

Class width =

Highest Score – Lowest Score
/.
Number of classes

Class width =

70 – 9
/.
6th

Class width =

61
/.
6th

= 10.166

Round 10,166 down to 10 and use 10 as the appropriate number for the class width.

Step 3:

The lowest value in the list is 9. Let’s use 9 as the lower limit of the first class.

To find the upper limit of the first class, subtract 1 from the class width and add the result to the lower limit of the first class.

10-1 = 9

9 + 9 = 18

Hence the first grade is 9-18

To find all of the lower bounds, just add the class width to the previous lower bound.

Lower limits (in bold)

9 + 10 = 19

19th + 10 = 29

29 + 10 = 39

39 + 10 = 49

49 + 10 = 59

Upper limits (in bold)

To find all of the caps, just add the class width to the previous cap.

18th + 10 = 28

28 + 10 = 38

38 + 10 = 48

48 + 10 = 58

58 + 10 = 68

Now all you have to do is count the frequency of these classes. For example, to find the frequency of 19-28, simply count all the numbers between 19 and 20, starting with 19 and ending with 28. Notice that the sum of all frequencies is 50.

## Construction of a frequency distribution, relative frequency and percentage distribution

The relative frequency and percentage can be found using the same formula we used in this lesson.

For example, the relative frequency of 9 is 9/50 = 0.18

To find the percentage, simply multiply 0.18 by 100

0.18 x 100 = 18

The percentage is 18%

The following table shows the frequency distribution, relative frequency, and percentage distribution for the above data set. Notice that the sum of all relative frequencies is 1 and the sum of all percentages is 100%