Frequency Tables

In a frequency table the data is grouped into classes. The number of pieces of data that fall into a particular class is called the frequency. Before we can set up the classes, we must find the smallest and largest values. Using the sorted data below, we see that the largest weight is 230 and the smallest is 82.

[Maple Math]

Since 230 minus 82 is 148, we say that the range is 148. We will use 7 classes in this example. Dividing 148 by 7, we get approximately 21.14. Round this up to 22. ( Note this is not rounding off .)

Our first class will start with 82. The start of each class will go up by 22. The lower class limits of the 7 classes are 82, 104, 126, 148, 170, 192, and 214.

Below is the frequency table using these lower class limits for this data. 

class        frequency  

--------------------------

 82. - 103.     2         

 104. - 125.    5         

 126. - 147.    11        

 148. - 169.    12        

 170. - 191.    8         

 192. - 213.    9         

 214. - 235.    3

Class Limits vs Class Boundaries

The first class has a lower class limit of 82 and an upper class limit of 103. This means that a weight w gets counted in this class if w is greater than or equal to 82 and less than or equal to 103. (i.e. 82 and 103 are the smallest and largest values allowed in the class.)

The first class has boundaries of 81.5 and 103.5 This means that a weight w gets counted in this class if w is greater than or equal to 81.5 and less than 103.5 (i.e. w is a number that rounds off to a number between 82 and 103 inclusive.)

For this example the lower class limits are

82, 104, 126, 148, 170, 192, and 214.

The upper class limits are

103, 125, 147, 169, 191, 213, and 235.

The class boundaries are 81.5, 103.5, 125.5, 147.5, 169.5, 191.5, 213.5, and 235.5.

Class Marks

The class mark is the midpoint of a class. It is obtained by dividing the sum of the lower class limit and upper class limit by 2. For this example the class mark for the first class is [Maple Math] = 92.5. The class marks for the other classes are 114.5, 136.5, 158.5, 180.5, 202.5, and 224.5.

Class Width

The class width is the difference between two consecutive lower class limits or two consecutive lower class boundaries. For the first class we get 104-82 = 22 (using two consecutive lower class limits) or 103.5-81.5 = 22 (using two consecutive lower class boundaries). The width of each of the other classes is also 22.

Note that consecutive class marks also differ by the class width.