Probability and Statistics Index>>Basic Statistics>How to find a five-number summary in statistics

## How to find a five-number summary in statistics: Overview

The five number summary consists of 5 items:

- The minimum.
- Q1 (the first quartile, or the 25% mark).
- The median.
- Q3 (the third quartile, or the 75% mark).
- The maximum.

The five number summary gives you a rough idea about what your data set looks like. for example, you’ll have your lowest value (the minimum) and the highest value (the maximum). Although it’s useful in itself, the main reason you’ll want to find a five-number summary is to find more useful statistics, like the interquartile range, sometimes called the middle fifty.

This how to article will guide you through how to find a five-number summary. Watch the video or read the steps below:

## How to Find a Five-Number Summary: Steps

**Step 1:***Put your numbers in ascending order*(from smallest to largest). For this particular data set, the order is:

Example: 1,2,5,6,7,9,12,15,18,19,27.**Step 2:***Find the minimum and maximum*for your data set. Now that your numbers are in order, this should be easy to spot.

In the example in step 1, the minimum (the smallest number) is 1 and the maximum (the largest number) is 27.**Step 3:***Find the median*. The median is the middle number. If you aren’t sure how to find the median, see: How to find the mean mode and median.**Step 4:***Place parentheses around the numbers***above and below**the median.

(This is not*technically*necessary, but it makes Q1 and Q3 easier to find).

(1,2,5,6,7),9,(12,15,18,19,27).**Step 5:***Find Q1 and Q3*. Q1 can be thought of as a median in the lower half of the data, and Q3 can be thought of as a median for the upper half of data.

(1,2,**5**,6,7)**, 9**, ( 12,15,**18**,19,27).**Step 6:***Write down your summary found in the above steps*.

minimum=1, Q1 =5, median=9, Q3=18, and maximum=27.

*That’s it! *

## Box and whisker chart

A box and whiskers chart is a visual representation of the summary.

## When the Summary doesn’t exist

Sometimes, it’s impossible to find a five number summary. In order for the five numbers to exist, your data set must meet these two requirements:

- Your data must be
**univariate**. In other words, the data must be a single variable. For example, this list of weights is one variable: 120, 100, 130, 145. IF you have a list of ages and you want to compare the ages to weights, it becomes bivariate. For example: age 1 (25 pounds), 5 (60 pounds), 15 (129 pounds). The matching pairs makes it impossible to find a five number summary. - Your data must be ordinal, interval, or ratio.

Like the explanation? Check out the Practically Cheating Statistics Handbook, which has hundreds more step-by-step solutions, just like this one!

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Now these questions I didn’t mind doing and they weren’t so mind bogging. I actually understood something for once. These kinds of problems anyone can do them, the information above is a lot more helpful then our book.

Even though this problem is kind of long, the problem and explanation itself was easy to do and easy to understand.

this helped me a million

i dont know why they dont teach it like this all the time,

simple

Thanx this is so much easier to remember I have a test on all this tommorrow so this is excellent help ;)

Thanks!!! :)

What about outliers?

In the *real* world, you’d probably discard them, if they look like statistical anomalies. On a test in class though, I’d go ahead and include them ;)

Stephanie

Really helpful to me, 50,000 times

This short explaination really helped.Thanks

So much easier than having to go book to my school books to have a look! Thanks.

thnxs but im still confused

Thanks so much for the easy explanation! I have been trying to get this and my teacher is of no help.

what happens when you break the numbers down to Q3 and Q1 but there are 2 medians?

Matt,

If you could post a specific example on the forum (click the tab up there ^^) then we’ll be better able to answer that.

Best,

Stephanie