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

Raw data

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.

Frequency distribution table

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.

Frequency distribution, relative frequency, and percentage distribution

Notice that the sum of all relative frequencies is 1 and the sum of all percentages is 100%






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