In mathematics grouping of data we will learn how to group data.
So far, we have considered ungrouped data. When the number of observations is large,
we may condense the data into several groups. We record the frequency of observations falling in each group.
Presentation of data in groups along with the frequency of each group is known as the frequency distribution of the grouped data.
Examples on grouping data are explained here in detailed stepbystep explanation.
Grouping of Data
1. The marks obtained by 40 students of class VIII in an examination are given below:
16, 17, 18, 3, 7, 23, 18, 13, 10, 21, 7, 1, 13, 21, 13, 15, 19, 24, 16, 2, 23, 5, 12,
18, 8, 12, 6, 8, 16, 5, 3, 5, 0, 7, 9, 12, 20, 10, 2, 23
Divide the data into five groups, namely, 05, 510, 1015, 1520 and 2025, where 05 means marks greater than or equal to 0 but less than 5 and similarly 510 means marks greater than or equal to 5 but less than 10, and so on. Prepare a frequency table for the grouped data.
Solution:
Arranging the given observations in ascending order, we get them as
0, 1, 2, 2, 3, 3, 5, 5, 5, 6, 7, 7, 7, 8, 8, 9, 10, 10, 12, 12, 12, 13, 13, 13, 15, 16, 16,
16, 17, 18, 18, 18, 19, 20, 21, 21, 23, 23, 23, 24
Thus, the frequency distribution may be given as under:
Note:
Here, each of the groups 05, 510, 1015, 1520 and 2025 is called a class interval.
In class interval 1015, the number 10 is called the lower limit and 15 is called the upper limit of the class interval.
The difference between the upper limit and the lower limit of any class interval is called the class size.
Thus, the class size in the above frequency distribution is 5.
The mid value of a class is called its class mark and is obtained by adding its upper and lower class limits and dividing the sum by 2.
Thus, the class mark of 05 is (0 + 5)/2 = 2.5
the class mark of 510 is (5 + 10)/2 = 7.5, etc.
2. The weights (in kg) of 35 persons are given below:
43, 51, 47, 62, 48, 40, 50, 62, 53, 56, 40, 48, 56, 53, 50, 42, 55, 52, 48, 46, 45, 54, 52, 50, 47, 44, 54, 55, 60, 63, 58, 55, 60, 58, 53
Prepare a frequency distribution table taking equal class size. One such class is 4045 (where 45 is not included).
Solution:
We may represent the data as given below:
Note:
Here, each of the data groups 4045, 4550, 5055, 5560 and 6065 is called a class interval.
● Data Handling
● Data Handling  Worksheet
8th Grade Math Practice
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