How to Find the Upper and Lower Limits of Class Intervals

J.D. asked about the way statisticians identify upper and lower limits of class intervals found in a variable's frequency distribution.  When data are comprised of interval/ratio numbers or class intervals, e.g., (20-29) (30-39) (40-49) and so on, the limits of such numbers or class intervals are understood in terms of “true (real) limits.”  True/real limits are defined by the highest possible value – the upper limit – and the lowest possible value – the lower limit. The general rules for calculating the true limits of class intervals represented by numbers are:

Upper True Limit:  Add a 5 to the decimal place to the right of the last number appearing in the highest value specified by the number in the class interval.

Lower True Limit:  Subtract a 5 to the decimal place to the right of the last number appearing in the lowest value specified by the number in the class interval.

If the class intervals of a variable are defined by whole numbers, to find the upper limit we add .5 to the highest value specified by the category, and to find the lower limit we subtract .5 from the lowest value specified in the category.  The limits of other numbers could be similarly determined.  The table below provides some illustrations.

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