What are class boundaries in statistics?

See explanation.

Class boundaries are true class limits.

Recall: Class limits are end numbers of a class interval.

For instance, we have a class interval ##1 - 5##. ##1## is called the lower limit (LL) and ##5## is the upper limit (UL). These numbers define a class. On the other hand, class boundaries were called true class limits. These are boundary points. They tend to bound the class limits.

Here's the definitional formula for class boundaries

• Upper-class boundary (UCB)

##"UCB" = "UL" + 1/2 "unit of measurement"##

• Lower class boundary (LCB)

##"LCB" = "LL" - 1/2 "unit of measurement"##

Let's take the class boundaries for the class interval ##1 - 5##. To do this, you need to determine the unit of measurement.

Since we are counting by "ones", ##1, 2, 3, 5##, and so on, then the unit of measurement is ##1## (a unit). So, we have to multiply ##1## by ##1/2## then we may now take the class boundaries

##"UCB" = 5 + (1/2)(1) = 5.5##

##"LCB" = 1 - (1/2)(1) = 0.5##

Therefore, the class boundaries are ##0.5 - 5.5##.

Let's try another example. Find the class boundaries for the given class interval: ##7.5 - 10.5##

Look at the least place value. In this example, we are counting by tenths. ##0.1, 0.2, 0.3, 0.4##, and so on, meaning that we have to multiply a tenth by ##1/2## to compute for the class boundaries.

##"UCB" = 10.5 + (1/2)(0.1) = 10.55##

##"LCB" = 7.5 - (1/2)(0.1) = 7.45##

So the required class boundaries are ##7.45 - 10.55##.

Happy new year! :D