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**.

0 – 10 10 – 20 20 – 30 |
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.**

0 – 10 11 – 20 21 – 30 |
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**

about The Math.