Statistics How To

How to Draw a Frequency Distribution Table

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How to Draw a Frequency Distribution Table: Overview

How to Draw a Frequency Distribution Table

One example of how to draw a frequency distribution table using tally marks to count items.


A frequency distribution table is one way you can organize data so that it makes more sense. For example, let’s say you have a list of IQ scores for a gifted classroom in a particular elementary school. The IQ scores are: 118, 123, 124, 125, 127, 128, 129, 130, 130, 133, 136, 138, 141, 142, 149, 150, 154. That list doesn’t tell you much about anything. You could draw a frequency distribution table, which will give a better picture of your data than a simple list.

How to Draw a Frequency Distribution Table: Steps.

Step 1: Figure out how many classes (categories) you need. There are no hard rules about how many classes to pick, but there are a couple of general guidelines:

  • Pick between 5 and 20 classes. For the list of IQs above, we picked 5 classes.
  • Make sure you have a few items in each category. For example, if you have 20 items, choose 5 classes (4 items per category), not 20 classes (which would give you only 1 item per category).

Step 2: Subtract the minimum data value from the maximum data value. For example, our IQ list above had a minimum value of 118 and a maximum value of 154, so:
154 – 118 = 36

Step 3: Divide your answer in Step 2 by the number of classes you chose in Step 1.
36 / 5 = 7.2

Step 4: Round the number from Step 3 up to a whole number to get the class width. Rounded up, 7.2 becomes 8.

Step 5: Write down your lowest value for your first minimum data value:
The lowest value is 118

Step 6: Add the class width from Step 4 to Step 5 to get the next lower class limit:
118 + 8 = 126

Step 7: Repeat Step 6 for the other minimum data values (in other words, keep on adding your class width to your minimum data values) until you have created the number of classes you chose in Step 1. We chose 5 classes, so our 5 minimum data values are:
118
126 (118 + 8)
134 (126 + 8)
142 (134 + 8)
150 (142 + 8)

Step 8: Write down the upper class limits. These are the highest values that can be in the category, so in most cases you can subtract 1 from the class width and add that to the minimum data value. For example:
118 + (8 – 1) = 125
118 – 125
126 – 133
134 – 141
142 – 149
150 – 157

Step 9: Add a second column for the number of items in each class, and label the columns with appropriate headings:

IQ Number
118-125
126-133
134-141
142-149
150-157

Step 10: Count the number of items in each class, and put the total in the second column. The list of IQ scores are: 118, 123, 124, 125, 127, 128, 129, 130, 130, 133, 136, 138, 141, 142, 149, 150, 154.

IQ Number
118-125 4
126-133 6
134-141 3
142-149 2
150-157 2

That’s How to Draw a Frequency Distribution Table, the easy way! Like the explanation? Check out our statistics how-to book, with a how-to for every elementary statistics problem type.

Tip: If you are working with large numbers (like hundreds or thousands), round Step 4 up to a large whole number that’s easy to make into classes, like 100, 1000, or 10,000. Likewise with very small numbers — you may want to round to 0.1, 0.001 or a similar division.

30 thoughts on “How to Draw a Frequency Distribution Table

  1. Iddi leveri

    Thanks for this wonderful explanations which have improved my understanding,and has helped me to acqure my degree on statistics with a good GPA,may god bless u.

  2. leKhA rOcKzzz

    hahhahaa…. WoNdERfuL iNfO… ThNKzzzzzzz…. A lOT YeAhhh i cn SaY It HeLpEd Me A LOt iN MaH ProJeCT… <3 <3 :) :) :) mAy GoD bLesss UUUUU THnKzzz oNce AgAin…

  3. Joseph Mwangi

    This is nice work. I have gone through it all and has enabled me to have a clear understanding of the topic.

  4. Stephanie

    Hi, Chola,

    I checked the steps and they are correct. I know that usually you would round 7.2 down (not up!) but for class width purposes you always round up.

    Stephanie

  5. Stat's Student

    Actually.. 7.2 would be rounded down, not up (because 2 is less than 5), therefore the number you would round 7.2 to would be 7, not 8.

  6. kenrosellc

    Hi, Stat’s Student,

    Technically, you *could* round down, but that would give you an unnecessary extra class. The rounding rules (round up if 5 or over, round down under 5) are really only adhered to in mathematical equations…especially when it comes to money. When it comes to figuring out class widths for a table — it really doesn’t matter (but most professors will round up to generate slightly larger class widths).

    In essence, does it really matter whether we end up with class widths of 7, or 8? Nope. The only thing it will affect is how your frequency table looks. It’s completely arbitrary — you could just look at the number (32) and say “oh, I’ll have a class width of 5…or 10).

    But trust me, your table will generally look best if you round UP. Try it both ways and see :)

    Stephanie

  7. peiqi

    Hmm i don’t understand for the step 10 part…why the numbers there suddenly a lot of digits ranges?

  8. Andale

    Well, nothing really happens. You’ll just end up with most likely an unusable table that doesn’t help you make sense of the data. Technically, you could have just one class. But the graph would be utterly useless!

  9. amer

    i think you have a mistake in step 8 and then followed in 9 and 10.

    the IQ range after 126-133 sholuld be the following
    134-141, 142-149, 150-157 and hence the frequency changes.

  10. Andale

    Hi, Teena,

    I’m not quite getting what you’re asking. It’s not really possible to have 5.29 classes. Could you rephrase your question?

    By the way, I don’t generally have much time to answer questions in the comments — you’ll have better luck posting in the statistics how to forums.

    Regards,
    Stephanie

  11. The Man

    Thanks, this makes more sense now my Professor had a hard time ex planing this to us. Now I understand it much more clearly.

  12. rosalie rellom

    its a very hard subject for me,,but i still study……….. further explanation , plss.. thanks

  13. Brenda Chambers

    trying to do a frequency distribution table with #’s like 2.32 and 4.64 for min & max so class width is .46 rounded up to 1. That’s fine until we get to step #8 for the upper limits & u subtract 1 then it’s 0. What to do next?

  14. Andale

    Brenda,

    For smaller numbers, pick divisions that are easier to work with. For example, instead of rounding to 1, try rounding to 1/2 (0.5).

    Stephanie

  15. Cidiqa

    working on an assignment. lecturers given us a set of very close numbers with max number 2.34 and min 2.05. the class widths 0.05 rounded up to 0.1. i have 6 classes (given) n i find that none of the numbers given fall into the last three classes. is that ok?