Mean, Mode, Median, and Range of Ungrouped and Grouped Data

​Grouped vs Ungrouped Data

An ungrouped frequency distribution is simply each data item listed in a table next to the frequency of the occurrence of that value. 

Ungrouped Frequency Distributions - used for data that can be enumerated and when the range of values in the data set is not large.

A grouped distribution is a way of organising a large set of data into smaller, more manageable groups.

A Grouped Frequency Distribution is used when the range of data values in the data set is large.

Example

Consider the marks obtained by students in an examination where the maximum marks of the exam are 100.

22, 65, 32, 36, 28, 17, 15, 64, 86, 52, 36, 55, 9, 48, 65, 96, 14, 6, 37, 69, 76, 49, 37, 46, 21, 67, 92, 98

If we create a frequency distribution table for each and every data item, then it will form a large table with one row for each data item

So for easy understanding, we can make a table with groups of data items

Class Intervals

• The data is grouped into classes. The table shown contains 10 classes

• Each class is recorded as a class interval so for example the 3rd class interval is 21-30

• Note that the class intervals do not overlap when working with discrete data

Class Limits

• The smallest and largest values of a class are called the class limits.

• Class limits are actual data values. 

• 21 and 30 are the class limits of the 3rd class interval

​Class Boundaries

• Class boundaries provide values that eliminate gaps between the class intervals

• Class boundaries are not actual data values

• To find a class boundary, average the upper class limit of one class and the lower class limit of the next class

• the class boundaries of the 3rd class are 20.5 and 30.5

Class width

• Each class interval has a class width

• The class width is the difference between the class boundaries

• The width of the class in the table shown is 30.5-20.5 = 10

Class Midpoint

• The class midpoint is calculated by finding the mean of the upper and lower class limits (or boundaries). 

​Video: https://youtu.be/zjHfAhcU6kE