Frequency Distribution
A frequency distribution is a tabular arrangement of data into classes according to the size or magnitude along with corresponding class frequencies (the number of values fall in each class).
Ungrouped Data or raw Data:
Data which have not been arranged in a systemic order is called ungrouped or raw data.
Grouped Data:
Data presented in the form of frequency distribution is called grouped data.
Array:
The numerical raw data is arranged in ascending or descending order is called an array.
Example:
Array the following data in ascending or descending order 6, 4, 13, 7, 10, 16, 19.
Solution:
Array in ascending order is 4, 6, 7, 10, 13, 16, and 19
Array in descending order id 19, 16, 13, 10, 7, 6, and 4
Class Limits:
The variant values of the classes or groups are called the class limits. The smaller value of the class is called lower class limit and larger value of the class is called upper class limit. Class limits are also called inclusive classes.
For Example: Let us take the class 10 – 19, the smaller value 10 is lower class limit and larger value 19 is called upper class limit.
Class Boundaries:
The true values, which describe the actual class limits of a class, are called class boundaries. The smaller true value is called the lower class boundary and the larger true value is called the upper class boundary of the class. It is important to note that the upper class boundary of a class coincides with the lower class boundary of the next class. Class boundaries are also known as exclusive classes.
For Example:
Weights in Kg |
No of Students |
60 – 65 |
8 |
65 – 70 |
12 |
70 – 75 |
5 |
25 |
A student whose weights are between 60kg and 64.5kg would be included in the 60 – 65 class. A student whose weight is 65kg would be included in next class 65 – 70.
Open-end Classes:
A class has either no lower class limit or no upper class limit in a frequency table is called an open-end class. We do not like to use open-end classes in practice, because they create problems in calculation.
For Example:
Weights (Pounds) |
No of Persons |
Below – 110 |
6 |
110 – 120 |
12 |
120 – 130 |
20 |
130 – 140 |
10 |
140 – Above |
2 |
Class Mark or Mid Point:
The class marks or mid point is the mean of lower and upper class limits or boundaries. So it divides the class into two equal parts. It is obtained by dividing the sum of lower and upper class limit or class boundaries of a class by 2.
For Example: The class mark or mid point of the class 60 – 69 is 60+69/2 = 64.5
Size of class Interval:
The difference between the upper and lower class boundaries (not between class limits) of a class or the difference between two successive mid points is called size of class interval.