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.

Click to Enlarge

27 comments:

  1. Thank you so incredibly much!

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  2. Thanks. Very explicit and helpful

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  3. ı sincerely thank u. At last , ı get it.

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  4. How do we find lower and upper real limits if we have the classes such as
    10-20
    20-30
    30-40
    40-50
    50-60
    Etc

    And
    10-12
    14-16
    18-20
    22-24
    Etc

    I need help on this.

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    Replies
    1. (14-12)/2=1
      Subtract 1 and add 1 for lower and upper limits respectively.

      For the first case do the same:
      (10-10)/2=0
      Subtract and add 0 for lower and upper limit respectively.

      Delete
    2. (14-12)/2=1
      Subtract 1 and add 1 for lower and upper limits respectively.

      For the first case do the same:
      (20-20)/2=0
      Subtract and add 0 for lower and upper limit respectively.

      Delete
  5. How to find lower and upper real limit in class interval like 10_20,20_30,30_40,40_50

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  6. How to find cumulative frequency to the given data.
    Class interval
    10-20
    20-30
    30-40
    40-50
    50-60

    Frequency
    4
    15
    25
    8
    6

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  7. Sets of numbers are:
    23,16,45,61,32,5,6,29
    What is the lower limit?

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  8. I need help on how to calculate percentile rank

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  9. What is the difference between apparent upper limit and real upper limit

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  10. Where can I place figure with more than 5 decimal .I.e on the next class interval or it remains on the same claws I nterval?

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  11. What is the highest class with the highest frequency?

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  12. how to find the lower and upper class limits in class interval 1_5,6_10,11_15,16_20,21_25,26_30,31_35,36_40

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  13. Please how do WE find the upper and lower class limit of
    Age. Freq

    0-9 3
    10-19. 6
    20-. 8
    30 10
    7
    I have been trying to solve and get the rest of the âge group in vain please help

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  14. What is the lower real limit of this class (14-18)

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