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%