Grouping of Data

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 step-by-step 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, 0-5, 5-10, 10-15, 15-20 and 20-25, where 0-5 means marks greater than or equal to 0 but less than 5 and similarly 5-10 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:

Grouping of Data



Note: Here, each of the groups 0-5, 5-10, 10-15, 15-20 and 20-25 is called a class interval.

In class interval 10-15, 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 0-5 is (0 + 5)/2 = 2.5

the class mark of 5-10 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 40-45 (where 45 is not included).

Solution:

We may represent the data as given below:


Note: Here, each of the data groups 40-45, 45-50, 50-55, 55-60 and 60-65 is called a class interval.


 Data Handling

Data Handling

Frequency Distribution

Grouping of Data


 Data Handling - Worksheet

Worksheet on Data Handling











8th Grade Math Practice

From Grouping of Data to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Counting Numbers from 1 to 50 | Match the Number | Missing Numbers

    Apr 04, 25 03:46 PM

    Math Coloring Pages on Counting Number Oredr
    In counting numbers from 1 to 50, recognize the numbers, count and then join the numbers in the correct number order. Here we mainly need eye-hand coordination to draw the picture and maintain the num

    Read More

  2. Counting Eleven to Twenty with Numbers and Words |Numbers from 11 - 20

    Apr 04, 25 03:21 PM

    Counting eleven to twenty with numbers and words are explained below. One ten and one more is eleven. Eleven comes after ten. One ten and two more is twelve. Twelve comes after eleven.

    Read More

  3. 5th Grade BODMAS Rule Worksheet | PEMDAS | Order of operations|Answers

    Apr 03, 25 03:11 PM

    5th Grade BODMAS Rule Worksheet
    In 5th Grade BODMAS Rule Worksheet you will get different types of problems on mathematical expressions involving different operations, mathematical expression with 'brackets' and 'of' and simplifying…

    Read More

  4. Worksheet on Simplification | Simplify Expressions | BODMAS Questions

    Apr 03, 25 02:58 PM

    Worksheet on Simplification
    In worksheet on simplification, the questions are based in order to simplify expressions involving more than one bracket by using the steps of removal of brackets. This exercise sheet

    Read More

  5. Divisible by 2 Video |Test of Divisibility by 2 Trick| Rules| Examples

    Apr 03, 25 10:25 AM

    Divisible by 2
    A number is divisible by 2 if the digit at unit place is either 0 or multiple of 2. So a number is divisible by 2 if digit at its units place is 0, 2, 4, 6 or 8.

    Read More