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Frequency Distribution

Raw Data

Raw data is a collection of initial observations, not yet organized. It is the information we get when we do survey.

 

Types of Data :-

It can be classified into two types.
(i) Discrete Data
(ii) Continuous Data

 

Discrete Data :-
Such data can be very precisely measured in whole numbers. The number of children in a family and size of shoes are some examples of discrete data.

 




Continuous Data

Such data can have any value between two whole numbers i.e. it cannot be measured with absolute accuracy. There will always be some error.

Weight of students in a class and temperature in a city are some examples of continuous data.

Frequency distribution table
Look at the following data. It tells you the performance grade of the students in a month.
 

6     5     6     9     7     4     2     4     7     8    3     4     9     8     2     3     5     9     7     8    9    7    5     6     7     7     4     4     7     8     3     4.
 

From this data, we know only the performance grade of the students in a month.

Let us form a table as follows.
 

Grade

Tally marks

Number of students(Frequency)

9 |||| 4
8 |||| 4
7 || 7
6 ||| 3
5 ||| 3
4 | 6
3 ||| 3
2 || 2
Total   32


This table shows clear picture of the given data. From this table, we come to know the number of students in each grade. This table is known as frequency distribution table.

The number of times a particular observation occurs in a given data is called its frequency. A frequency distribution shows how frequently a particular item occurs, in a group.

Frequency distribution table using class intervals
If the number of items is few, we can list them out as in the previous examples. If number of items is large, it is hard to list them out individually. In this case, we use class intervals to form frequency distribution table.

Let us see how to form the frequency distribution table using class intervals in the following
 

Example : Given below are marks scored by 30 children in a class, in mathematics.

90, 56, 23, 45, 21, 56, 34, 98, 90, 90, 45, 34, 45, 34, 23, 12, 3, 14, 45, 12, 14, 12, 75, 75, 5, 56, 56, 56, 56, 98.

 

The following points should be kept in mind, before grouping data into class intervals.

1. When you group data into class intervals, the most important factor that you have to take into consideration, is the range of the distribution. Find out the difference between the largest and the smallest observations.

Largest value = 98. Minimum value = 3. Range = 98 – 3 = 95.
 

2. The number of class intervals should not be too many. At the same time, they should not be too few in number. There could be from 5 to about 20 class intervals.
 

3. Based on the above two factors, you will have to choose the width of the class intervals. You should choose this width with great care. It should not be so wide, that the significance of the data is lost; nor should it be so narrow that the number of intervals is too many. Only you can decide the optimum size of the interval.

Let us take the width as 20.
 

Frequency distribution of marks of 30 students in mathematics

Class interval

Tally marks

Frequency

0 - 20

||

7

20 - 40

|

6

40 - 60

10

60 - 80

||

2

80 - 100

5


1. The number on the left of class intervals is called the lower class limit and the one on the right is the upper class limit.

2. The difference between the two limits, gives you the width of the interval or the class size.

3. The mid value of each class interval is called its class mark. It is obtained by adding the lower and upper class limits and dividing the sum by 2.

 

Example : 

Consider the interval 20 – 40

Lower limit of the interval = 20

Upper limit of the interval = 40

Width of the interval = 40 – 20 = 20

Class mark =  =  = 30

 

By looking into the table, we can get some information:

1) Number of students who scored less than 50 marks.

2) Number of students who passed.

3) Number of students who scored above 80.

4) We can identify the performance of the class.
 

The method of classifying data into class intervals is called grouping of data.

 

Two Different Types of Class Intervals
There are two different types of class intervals

(i) overlapping class intervals 
(ii) non-overlapping class intervals

Non-overlapping intervals like 0- 19, 20 - 39, 40 - 59, etc., are so called,  since the upper limit of the previous class, and the lower limit of the next one are different. This kind of class interval is only useful for discrete data.

In overlapping class intervals the upper limit of the previous class is the same as the lower limit of the next one.
 

Example

0 - 20, 20 - 40, 40 - 60, etc. The problem that arises here is where will you put down the score 40? Will it be in the interval 20 - 40 or 40 - 60?

Solution

20 - 40, means all data up to 40, but not including 40. Hence, 40 will go to the 40 - 60 group. This is convenient for continuous data since heights and weights cannot be measured accurately. If the height is 160 cm, it would not go into the 140 - 160 group, but will go into the 160 - 180 group. With this rule we can also use overlapping intervals for discrete data.





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