LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

FREQUENCY OF DISTRIBUTION - GROUPED DATA

**Grouped
Date –**

**To put the data in a more condensed or intact form, we
need to make groups of suitable size, and should mention the frequency of each and
every group. That kind of table is to be considered or called as a grouped frequency distribution table. **

__Class Interval –__ If into each group where the raw data is condensed or accumulated or
collected intactly, is called or considered as a class-interval. Each class
would be bounded by two figures, which are called or considered as class
limits. The figure on the left side of a class is called or considered of its lower limit and that on its right is called its upper limit.

**Types of
Grouped Frequency Distribution –**

__1) Exclusive Form (or Continuous Interval Form) :__ A frequency distribution in
which or where the upper limit of each class will be excluded and lower limit
will be included, and this will be called an exclusive form.

**Example :
Suppose the marks obtained by some students in an examination are given. We may
consider the classes 0 – 10, 10 – 20, etc. In class 0 – 10, we include 0 and
exclude 10. In class 10 – 20, we include 10 and exclude 20.**

__2) Inclusive Form (or Discontinuous Interval Form) :__ A frequency distribution in
which each upper limit as well as lower limit is included, is called an
inclusive form. Thus, we have classes of the form 0 – 10, 11 – 20, 21 – 30,
etc. In 0 – 10, both 0 & 10 are included.

**Example.1) Given below are the marks obtained by 60
students in an examination: -**

**3,
25, 48, 23, 17, 13, 11, 9, 46, 41, 37, 45, 10, 19, 39, 36, 34, 5, 17, 21, 39,
33, 28, 25, 12, 3, 8, 17, 48, 34, 15, 19, 32, 32, 19, 21, 28, 32, 20, 23, 25,
27, 32, 37, 19, 32, 26, 29, 24, 30, 37, 23, 32, 43, 47, 29, 49, 31, 45, 37.**

**Arrange
the data in ascending order and present it as a grouped data in ;**

**a)
Discontinuous interval form, taking class intervals 1 – 10, 11 – 20, etc.**

**b)
Continuous Interval form, taking class intervals 1 – 10, 10 – 20, etc.**

**Solution:- Arranging the above given numbers or marks in ascending order, and we get –**

**3, 3, 5, 8, 9, 10, 11, 12, 13, 15, 17, 17, 17, 19, 19, 19, 19, 20, 21,
21, 23, 23, 23, 24, 25, 25, 25, 26,
27, 28, 28, 29, 29, 30, 31, 32, 32, 32, 32, 32, 32, 33,
34, 34, 36, 37, 37, 37, 37, 39, 39, 43, 47, 41, 45, 45, 46, 48, 48, 49**

**Now we may
classify them into groups as shown below – **

**a) Discontinuous Interval Form (or
Inclusive Form) –**

**
**

**Note that –
the class 1 – 10 means, marks obtained from 1 to 10, including both. Same is
applicable for other group also.**

**b) Continuous Interval Form (or Exclusive Form)**

**Note that –
the class 1 – 10 means, marks obtained from 1 to 9, excluding 10. Same is
applicable for other group also.**