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

Watch the video for an instance of how to discover a 5 number summary for an odd collection of numbers:
Can’t see the video? Click below.

You are watching: A distribution of numbers has the following five number summary

This second brief video mirrors what to execute if you have an even set of numbers:

The 5 number summary includes 5 items:

The minimum.The maximum.

The 5 number summary gives you a unstable principle about what your data collection looks like. for instance, you’ll have your lowest worth (the minimum) and the highest possible worth (the maximum). Although it’s helpful in itself, the primary reason you’ll desire to discover a five-number summary is to find even more helpful statistics, choose the interquartile selection, sometimes called the middle fifty.

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How to Find a Five-Number Summary: Steps

Step 1: Put your numbers in ascending order (from smallest to largest). For this certain data set, the order is:Example: 1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27.Step 2: Find the minimum and also maximum for your data set. Now that your numbers are in order, this need to be easy to spot.In the example in action 1, the minimum (the smallest number) is 1 and also the maximum (the largest number) is 27.Step 4: Place parentheses about the numbers above and below the median. (This is not technically essential, but it provides Q1 and Q3 simpler to find).(1, 2, 5, 6, 7), 9, (12, 15, 18, 19, 27).Tip 5: Find Q1 and Q3. Q1 have the right to be assumed of as a median in the reduced half of the information, and also Q3 can be thought of as a median for the top half of data.(1, 2, 5, 6, 7), 9, ( 12, 15,18,19,27).Tip 6: Write down your summary found in the over steps.minimum = 1, Q1 = 5, median = 9, Q3 = 18, and also maximum = 27.

That’s it!

When the Rundown doesn’t exist

Sometimes, it’s difficult to find a five-number summary. In order for the five numbers to exist, your data collection should accomplish these two requirements:

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Box and also whisker chart

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

Box Plot / Find a Five-Number Synopsis on the TI 89


A left skewed boxplot, showing a long left whisker. Image: SHU.EDU

When you develop a box and also whiskers chart on the TI-89, the TI-89 will instantly calculate the five number summary for you.

Example problem: Create a box and also whiskers chart and discover the 5 number summary for the following data: 200, 350, 300, 350, and 400.

Step 1: Create a brand-new folder called “Box.” From the HOME screen, press F4 and also scroll dvery own to NewFold (choice B). Press ENTER.

Tip 2: Press second Alpha ( – x to spell B O X and also press ENTER.

Tip 3: Press APPS, then scroll dvery own to Stats/List Editor. Press ENTER twice.

Tip 4: Press the dvery own arrowhead key to obtain to the initially line of the list. Enter your data into list1. Follow each entry via a comma: 200, 350, 300, 350, 400.

Tip 5: Press F2 then 1 to enter Plot Setup.

Tip 6: Press F1, right arrowhead, and also 5 to pick mod box plot.

Step 7: Arrow down to Mark and also pick box.

Step 8: Arrow dvery own and enter B O X (making use of the alphanumeric keypad) in the x. Press ENTER.

Tip 9: Read the boxplot. Press F3 and use the left and appropriate cursors to uncover Min(200), Q1(250), Med(325), Q3(400), and also Max(500).

That’s it!

Tip: if you want to readjust the folder ago to MAIN, press MODES, scroll down to Current Folder. Press best key, then push 1 ENTER.

TipIf you gain the error message undefined variable, it deserve to be a frustrating process to attempt and fix the trouble. Clearing the memory *may* help, but an much easier method to gain package plot to graph is to enter the data into “list 1” in the List Editor and then type “list 1” as your “x” as soon as defining package plot.

Lost your guidebook? You deserve to downpack a new one from the TI webwebsite below.Back to Top

Find a Five Number Overview in SPSS

Calculating the five number summary is pretty straightforward if you have actually a small data collection, yet for bigger data sets — which you will certainly typically job-related through in SPSS — the job deserve to be imperhaps tedious. That’s wbelow software application prefer SPSS comes in handy — tasks that would certainly sometimes take hours by hand deserve to be calculated in a fraction of a 2nd. The SPSS five number summary is calculated via the “Frequencies” tool.

Watch the video for the steps:
Can’t view the video? Click below.

Step 1: Open a new information sheet and also form your data into a column (or numerous columns). To open up a brand-new data sheet, click “File” in the toolbar, then click “new” and then click “Documents.” Make certain you kind your information without spaces (in various other words, don’t leave empty rows).

Tip 2: Click “Analyze,” then click “Descriptive Statistics” and then click “Frequencies” to open the Frequencies dialog box.


The five number summary in SPSS is calculated with the Frequency food selection.

Step 3: Click a variable name (or several if you have actually gone into your information right into multiple columns) and then click the central arrow to relocate them to the Variable(s) list box. Note that SPSS supplies the term “Variables,” yet all it really implies is the column header name. You can readjust this name by clicking the “Variables” watch button at the bottom of the sheet.

Tip 4: Click “Statistics” to open the Statistics dialog box.

Tip 5: Check “Quartiles,” “median,” “minimum” and also “maximum” and then click “Continue.”

Step 6: Click “OK”. The SPSS five number summary is calculated and the results are returned in a brand-new window.

Note: SPSS lists the initially quartile (Q1) as the 25th percentile in the results home window, and the 3rd quartile (Q3) is noted as the 75th percentile.Back to Top

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Larry Gonick. The Cartoon Guide to Statistics, 1993David C. Hoaglin, Frederick Mosteller and also John W. Tuvital. “Understanding durable and exploratory data analysis“. Wiley, 1983.

CITE THIS AS:Stephanie Glen. "Find a Five-Number Summary in Statistics: Easy Steps" From Elementary Statistics for the remainder of us!

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