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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27 comments:

  1. UnknownDecember 7, 2014 at 6:49 AM

    thanks! really helped me!

    ReplyDelete
  2. UnknownAugust 23, 2015 at 8:19 AM

    i just saw the light...thanks

    ReplyDelete
  3. MunamiOctober 4, 2015 at 5:42 PM

    Thank you so incredibly much!

    ReplyDelete
  4. RotimiFebruary 16, 2016 at 7:37 PM

    Thanks. Very explicit and helpful

    ReplyDelete
  5. UnknownOctober 26, 2016 at 7:23 PM

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

    ReplyDelete
  6. UnknownJuly 15, 2017 at 6:45 AM

    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.

    ReplyDelete
    Replies
    1. VlogsJanuary 22, 2021 at 10:57 PM

      Ul-20
      Ll-10

      Delete
    2. UnknownSeptember 26, 2021 at 7:15 AM

      Gadhe

      Delete
    3. PeterNovember 22, 2021 at 7:12 AM

      (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
    4. PeterNovember 22, 2021 at 7:13 AM

      (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
  7. UnknownOctober 16, 2018 at 9:00 PM

    Thnx this would help me

    ReplyDelete
  8. UnknownMay 31, 2019 at 4:24 AM

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

    ReplyDelete
  9. UnknownApril 15, 2020 at 10:39 PM

    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

    ReplyDelete
  10. UnknownApril 28, 2020 at 3:28 AM

    Thanks it really helped me

    ReplyDelete
  11. UnknownOctober 28, 2020 at 8:52 PM

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

    ReplyDelete
  12. UnknownNovember 19, 2020 at 6:50 PM

    How do you find upper limits

    ReplyDelete
  13. UnknownNovember 21, 2020 at 4:11 AM

    I need help on how to calculate percentile rank

    ReplyDelete
  14. UnknownDecember 10, 2020 at 1:39 PM

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

    ReplyDelete
  15. SelemaniJanuary 11, 2021 at 11:04 PM

    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?

    ReplyDelete
  16. UnknownMarch 8, 2021 at 10:11 PM

    Very nice

    ReplyDelete
  17. TayoMarch 25, 2021 at 1:04 PM

    Short,simple and meaningful

    ReplyDelete
  18. UnknownJune 21, 2021 at 11:54 PM

    What is the highest class with the highest frequency?

    ReplyDelete
  19. UnknownJuly 1, 2021 at 4:40 AM

    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

    ReplyDelete
  20. UnknownSeptember 23, 2021 at 9:26 PM

    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

    ReplyDelete
  21. UnknownOctober 4, 2021 at 5:52 AM

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

    ReplyDelete
  22. TechRashidNovember 22, 2021 at 10:34 PM

    Thanks that helped me

    ReplyDelete

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