Data values are classified into classes with equal widths. Class limits are the lowest and greatest observations in each class, whereas class boundaries are values midway between the upper class limit of one class and the lower class limit of the next. And what is the difference between a class boundary and a class limit?
Let’s look at the image below to see the difference between class limit and class boundary.
The upper extreme value of the first class interval and the lower extreme value of the second class interval will not be identical in class limit.
The upper extreme value of the first class interval and the lower extreme value of the following class interval will be equal at the class border.
Let’s look at the frequency distribution of weights of 36 students to learn more about class limit and class boundary.
Class limits are the least and highest values that may be found in a class interval.
The smallest amount is known as the lower class limit (LCL), while the highest value is known as the upper class limit (UCL) (UCL).
The LCL and UCL of the first class interval for the frequency distribution of weights of 36 students are 44 kgs. and 48 kgs., respectively.
Class boundary are the real class limits of a class interval.
Class boundaries correspond with class limits in overlapping classification or mutually exclusive class boundary that excludes higher class limits such as 10–20, 20–30, 30–40, etc.
This is often done using a continuous variable. However, for non-overlapping or mutually inclusive categorization that covers both class boundaries such as 0–9, 10–19, 20–29,…… that is often applicable for a discrete variable, we have
where D is the difference between the following class interval’s LCL and the given class interval’s UCL.
For the data in the preceding table, the LCB of the first class interval is
and the corresponding UCB
Aside from the obvious class limit and class boundary, consider the midpoint of a class interval.
This corresponds to a class interval and is defined as the sum of the two class limits or class boundary divided by two.
In other words, in a class interval, the mid point or mid value may be defined as the arithmetic mean or average of the two class limits and two class boundary.
As a result
The mid-points for the first two class intervals are based on the weight distribution of 36 pupils.
That is, 46 and 51 kg, respectively.
Class borders are the numbers that are used to divide classes. The amount of the class gap is the difference between one class’s upper class limit and the following class’s lower class limit. In this scenario, gap=21.8321.82=0.01 gap = 21.83 – 21.82 = 0.01 gap = 21.83 – 21.82 = 0.01
The class limits, which correspond to a class internal, may be defined as the lowest and maximum values that the class interval can hold. The lower class limit (LCL) is the lowest value, while the upper class limit (UCL) is the highest amount (UCL) Ex.
As a result, this term is used interchangeably with bound. The true meaning, however, is a visible symbol denoting a boundary. Bound is the limit itself or the farthest point of expansion, and it might be an imaginary line; nonetheless, boundary is the object that determines the limit; terminus, not finis.
Class limits are derived in inclusive form by subtracting 0.5 from the lower limit and adding 0.5 to the higher limit. Thus, the inclusive class boundaries of the 10 – 20 class interval are 9.5 – 20.5. The class size is the difference between the actual upper and true lower limits of a class interval.
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