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. Expanded form of Decimal Fractions |How to Write a Decimal in Expanded

    Jul 22, 24 03:27 PM

    Expanded form of Decimal
    Decimal numbers can be expressed in expanded form using the place-value chart. In expanded form of decimal fractions we will learn how to read and write the decimal numbers. Note: When a decimal is mi…

    Read More

  2. Worksheet on Decimal Numbers | Decimals Number Concepts | Answers

    Jul 22, 24 02:41 PM

    Worksheet on Decimal Numbers
    Practice different types of math questions given in the worksheet on decimal numbers, these math problems will help the students to review decimals number concepts.

    Read More

  3. Decimal Place Value Chart |Tenths Place |Hundredths Place |Thousandths

    Jul 21, 24 02:14 PM

    Decimal place value chart
    Decimal place value chart are discussed here: The first place after the decimal is got by dividing the number by 10; it is called the tenths place.

    Read More

  4. Thousandths Place in Decimals | Decimal Place Value | Decimal Numbers

    Jul 20, 24 03:45 PM

    Thousandths Place in Decimals
    When we write a decimal number with three places, we are representing the thousandths place. Each part in the given figure represents one-thousandth of the whole. It is written as 1/1000. In the decim…

    Read More

  5. Hundredths Place in Decimals | Decimal Place Value | Decimal Number

    Jul 20, 24 02:30 PM

    Hundredths Place in Decimals
    When we write a decimal number with two places, we are representing the hundredths place. Let us take plane sheet which represents one whole. Now, we divide the sheet into 100 equal parts. Each part r…

    Read More