# stats 28

(As this blog site does not support the formatting, there could be errors in the post.

This series is compiled from various resources on net. I have made changes wherever necessary to make it simple to understand. )

Table: Frequency distribution of heights of 50 students

Height Frequency (Number of students)

144.5-146.5 2

146.5-148.5 5

148.5-150.5 8

150.5-152.5 15

152.5-154.5 9

154.5-156.5 6

156.5-158.5 4

158.5-160.5 1

Total 50

Class, class limits, class boundaries

The interval defining a class is known as a class interval. 145-146,147-148,… are class intervals. The end numbers 145 and 146 of the class interval 145-146 are known as class limits. The smaller number 145 is the lower class limit and the larger number 146 is the upper class limit.

When we refer to the heights being recorded to the nearest centimeter and consider a height between 144.5(greater or equal to 144.5 but less than 146.5) as falls in that class and the class is represented as the 144.5 146.5,the end number are called class boundaries, the smaller number 144.5 is known as lower class boundary and the larger number 146.5 as upper class boundary. The difference between the upper and lower class boundaries is known as the width of the class. Here the width is 146.5 – 144.5 = 2 cm and is the same for all the classes. The common width is denoted by c or w. Here c or w = 2 cm. Note that in certain cases, it may not be possible to have the same width for all the classes.

Note also that the upper class boundary of a class coincides with the lower class boundary of the next class; there is no ambiguity: we have clearly indicated that an observation less than 146.5 will fall in the class 144.5-146.5 and an observation equal to 146.5 will fall in the class 146.5-148.5.

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