Probability and Statistics > Descriptive Statistics > How to Draw a Frequency Distribution Table

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## How to Draw a Frequency Distribution Table: Overview

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).

Note: There is a more mathematical way to choose classes. The formula is log(observations)\ log(2). You would round up the answer to the next integer. For example, log17\log2 = 4.1 will be rounded up to become 5. (Thank you to Ayman Masry for that tip).

**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 hundreds more step by step solutions, just like this one!

**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.

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

HEY!…step # 3 is wrong it must 7 because 7.2 it doesn’t become 8…

but it is a challenge work for us…it is nice…whose work this…KEEP UP THE GOOD WORK!…:D

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

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.

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

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

What happens if no. Of classes are less than 5 & more than 20

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!

Peiqi,

That was a hiccup in the html, which is now fixed.

Thanks!

Stephanie

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.

Amer,

You’re right…that should be a 142, not 141! It’s now fixed.

Thanks,

Stephanie

if no. of classes are 5.29 than it would round off to which no. 9 or 8?

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

its a very easy way to understand this topic………..thanks mam……….:D

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

Great! Glad I could help :)

Thanks A lot!

thanks for your help !! i didnt know but now i know >>

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

VERY NICE CONTANT

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?

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

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?

Cidiqa,

Unfortunately, time constraints prevent me from answering stats related questions on the comments section. But please ask for help on our forums — one of our moderators will be glad to help!

http://www.statisticshowto.com/forums/

Stephanie

thanks a lot…….

I understood the topic very clearly!!!!

i love it..it is such very educative

I was so confused but this article helped me alot

Do you choose any number between 5-20 for frequency f or the is a formula for it,um stuck pls help

Choose a number that works for your data. The goal is to show a nice, clear graph of your output. How many data points do you have?