Definition
Inclusive and exclusive class intervals
Statistics • Frequency Distribution • Class Interval
Statement
Classes written , , are INCLUSIVE: both stated limits belong to the class, and a gap is left between one upper limit and the next lower limit. Classes written , , are EXCLUSIVE: consecutive classes share a limit, and the shared value is counted in the class for which it is the LOWER limit, so the upper limit is excluded. An inclusive distribution is made continuous by subtracting half the gap from every lower limit and adding it to every upper limit, giving class boundaries , and so on.
How to use it
- 1Decide which family you are looking at by asking whether two consecutive classes share an endpoint: shared means exclusive, a gap means inclusive.
- 2Convert an inclusive distribution to boundaries before drawing a histogram or computing a median, a mode or anything else obtained by interpolation; leaving the gaps in distorts every one of them.
- 3The class width of an inclusive class is the boundary width - for it is , not .
Worked example
Write the class boundaries of the inclusive classes , , .
Step-by-step
- 1
Why: Half the gap is shared out between the two neighbouring classes.
- 2
Why: Every lower limit falls by and every upper limit rises by .
Answer
, ,
Watch out
The two names are routinely stated the wrong way round. 'Exclusive' refers to the UPPER limit being excluded, which is only possible when the next class claims it - that is, when consecutive classes share a boundary. Data recorded to the nearest unit need a correction of , data recorded to one decimal place a correction of .