Question

Define class limits.

Answer 1

Hint: We recall the difference between ungrouped data and grouped data. The groups have to be divided into categories or intervals called classes. The left of limit of the class interval is the lower class limit, the smallest value that can enter into a class and right limit is called upper class limit, the largest value that can enter into a class.

Complete step by step answer:
We know that raw data otherwise known as ungrouped data is the data which has not been placed in any categories and no aggregation or summarization has taken place on the data. Ungrouped data is directly obtained from the source, for example the data of marks of 10 students 7,12, 15, 25, 26, 35, 37, 39, 41, 42, 49, 49. Each value of the data is called data value or observation. The whole data is called a data sample.
If we divide the data sample into closed intervals without leaving any single data value then the intervals are called classes or bins, for example let us divide the data of the students into 5 intervals say 1-10, 11-20, 21-30,31-40,41-50 which will contains data values 7, (12, 15), (25, 26), (35, 37, 39), (41, 42, 49, 49) respectively.
We see that like all intervals classes have a left limit which is the smallest value in the interval and right limit which is the largest value in the interval. The left limit of the is called lower class limit and right limit is called upper class limits of the class. Together they are called class limits of the class. If we define a class interval $I$ as $I=l-u$ or $I=\left[ l,u \right]$ then the class limits are
\[\begin{align}
  & \text{lower class limt }=l \\
 & \text{upper class limt }=u \\
\end{align}\]
 The lower class limits of the student mark classes 01-10, 10-20, 20-30,30-40,40-50 are
\[l=1,11,21,31,41\]
The upper class limits of the student mark classes 0-10, 10-20, 20-30,30-40,40-50 are
\[u=10,20,30,40,50\]

Note:
Number of data values that lie inside a class is called frequency. The difference between class limits is called width $w=u-l$ and the class width may not be equal for classes. The average of class limits is called class mark $m=\dfrac{u+l}{2}$, the average of all lower class limits of the data sample is called lower class boundary and the average of all upper class limits is called upper class boundary.