If the data set is large, rather than record the frequency for each value a random variable $X$ can take in an experiment, often data will be grouped into classes.
The class intervals are the subsets into which the data is grouped. The width of the class intervals will be a compromise between having intervals short enough so that not all of the observations fall in the same interval, but long enough so that you do not end up with only one observation per interval. It is also important to make sure that the class intervals are mutually exclusive.
With discrete data we may group by choosing convenient values. For example, in recording the number of runs cricketers score in a Test Match we might use the intervals $0$ to $9$, $10$ to $19$, $20$ to $29$ etc.
Continuous data may, in theory, take any real value. Here we use appropriate inequalities to ensure that the class intervals are mutually exclusive. For example, in recording the height $h$ (in metres) for a group of students we might use the intervals $1 \leq h < 1.2$, $1.2 \leq h <1.4$, $1.4 \leq h <1.6$ etc.
The lower boundary is the lower endpoint that determines the class interval; the upper boundary is the highest value.
A class of $30$ students measured their heights, $h$ (in meters), with the following results.
|
Height |
Frequency |
|---|---|
|
$155\leq h<165$ |
$3$ |
|
$165\leq h<175$ |
$9$ |
|
$175\leq h<185$ |
$15$ |
|
$185\leq h<195$ |
$3$ |
|
$195\leq h<205$ |
$1$ |
Find the lower boundary, upper boundary and class interval of the $175 \leq h <185$ class.
The lower boundary of the $175 \leq h < 185$ class is $175$ and the upper boundary is $185$. The class interval used was $175 - 185$.
This is a video on class intervals and boundaries produced by Alissa Grant-Walker.