Frequency Distribution of
Ungrouped and Grouped Data

Frequency distribution of ungrouped and grouped data is discussed below with examples.

Frequency distribution of ungrouped data:

Given below are marks obtained by 20 students in Math out of 25.

21, 23, 19, 17, 12, 15, 15, 17, 17, 19, 23, 23, 21, 23, 25, 25, 21, 19, 19, 19

Frequency distribution of grouped data:

The presentation of the above data can be expressed into groups. These groups are called classes or the class interval.

Each class interval is bounded by two figures called the class limits.

Marks

0 - 10

10 - 20

20 - 30

Number of Students
(Frequency)

0

11

9

Note: The lower value of a class interval is called lower limit and upper value of that class interval is called the upper limit. Thus, each class interval has lower and upper limits.

For Example:

In the class interval 10 - 20, 10 is the lower limit and 20 is the upper limit.


Exclusive form of data:

This above table is expressed in the exclusive form.

In this, the class intervals are 0 - 10, 10 - 20, 20 - 30. In this, we include lower limit but exclude upper limit.

So, 10 - 20 means values from 10 and more but less than 20.

20 - 30 would mean values from 20 and more but less than 30.


Data in the inclusive form:

Marks obtained by 20 students of class VIII in Math text are given below.

23, 0, 14, 10, 15, 3, 8, 16, 18, 20, 1, 3, 20, 23, 24, 15, 24, 22, 14, 13

Let us represent this data in the inclusive form.

Marks

0 - 10

11 - 20

21 - 30

Number of Students
(Frequency)

6

9

5

Here, also we arrange the data into different groups called class intervals, i.e., 0 - 10, 11 - 20, 21 - 30.

0 to 10 means between 0 and 10 including 0 and 10.

Here, 0 is the lower limit and 10 is the upper limit. 11 to 20 means between 11 and 20 including 11 and 20.

Here, 11 is the lower limit and 20 is the upper limit.

When the data is expressed in the inclusive form, it is converted to exclusive form by subtracting 0.5 from lower limit and adding it to upper limit of each class interval.

11 - 20 is expressed in the inclusive form which can be changed and taken as 10.5 - 20.5 which is the exclusive form of the data.

Similarly, 21 - 30 can be taken as 20.5 - 30.5.

The above illustrative examples on frequency distribution of ungrouped and grouped data are explained above to get the clear concept.

Statistics


From Frequency Distribution of Ungrouped and Grouped Data to

HOME PAGE

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.



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.



Share this page: What’s this?

Recent Articles

  1. Properties of Multiplication | Multiplicative Identity | Whole Numbers

    Mar 29, 24 09:02 AM

    Properties of Multiplication of Whole Numbers
    There are six properties of multiplication of whole numbers that will help to solve the problems easily. The six properties of multiplication are Closure Property, Commutative Property, Zero Property…

    Read More

  2. Multiplication of a Number by a 3-Digit Number |3-Digit Multiplication

    Mar 28, 24 06:33 PM

    Multiplying by 3-Digit Number
    In multiplication of a number by a 3-digit number are explained here step by step. Consider the following examples on multiplication of a number by a 3-digit number: 1. Find the product of 36 × 137

    Read More

  3. Multiply a Number by a 2-Digit Number | Multiplying 2-Digit by 2-Digit

    Mar 27, 24 05:21 PM

    Multiply 2-Digit Numbers by a 2-Digit Numbers
    How to multiply a number by a 2-digit number? We shall revise here to multiply 2-digit and 3-digit numbers by a 2-digit number (multiplier) as well as learn another procedure for the multiplication of…

    Read More

  4. Multiplication by 1-digit Number | Multiplying 1-Digit by 4-Digit

    Mar 26, 24 04:14 PM

    Multiplication by 1-digit Number
    How to Multiply by a 1-Digit Number We will learn how to multiply any number by a one-digit number. Multiply 2154 and 4. Solution: Step I: Arrange the numbers vertically. Step II: First multiply the d…

    Read More

  5. Multiplying 3-Digit Number by 1-Digit Number | Three-Digit Multiplicat

    Mar 25, 24 05:36 PM

    Multiplying 3-Digit Number by 1-Digit Number
    Here we will learn multiplying 3-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number. 1. Multiply 201 by 3 Step I: Arrange the numb…

    Read More