ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Box plots. How to draw a box plot from a list of data values (with no outliers)

Updated on September 17, 2011


To be able to draw a box plot you will need 5 values; the lowest value, the lower quartile (LQ), the median, the upper quartile (UQ) and the highest value. If you have a list of numbers then you will need to calculate these values before you can draw the box plot. Make sure the numbers are ordered from smallest to largest before you start.

If you have n values in your list then to find the lower quartile work out ¼ of n. If you get a decimal then round this number up and count along your data values until you reach this number. If you get a whole number then the LQ will be situated between this number and the next along your list of data values.

To calculate the median find ½ of n. If you get a decimal then round this number up and count along your data values until you reach this number. If you get a whole number then the median will be situated between this number and the next along your data values.

To calculate the UQ work out ¾ of n. If you get a decimal then round this number up and count along your data values until you reach this number. If you get a whole number then the UQ will be situated between this number and the next along your data values.

Let’s take a look at an example:

A group of 10 students take a geography test. Their results are:

54%, 68%, 87%, 24%, 39%, 59%, 61%, 89%, 17%, 32%

Draw a box plot to represent their test scores.

First you need to sort the numbers in size order (starting with the smallest value):

17%, 24%, 32%, 39%, 54%, 59%, 61%, 68%, 87%, 89%

Now calculate the 5 values you need for your box plot:

The lowest value is 17% (the first value in the list)

The lower quartile is ¼ of 10 = 2.5 = 3 (round up). So count three numbers in which gives LQ = 24%

The median is ½ of 10 = 5. So the median is between the 5th and 6th value = 57.5%

The upper quartile is at ¾ of 10 = 7.5 = 8 (round up) So count eight numbers in which gives UQ = 68%

The highest value is 89% (the last value in the list)

All you need to do now is draw a horizontal axis for the test scores. Go from 0% to 100%. All you need to do know is mark these five values above the axis. Make a box with the LQ, median and UQ and have 2 horizontal lines coming out from the LQ and UQ to the lowest and highest values on the box plot.

Sometime outliers can be marked on the box plot as well. But you will only have to do this if you are studying a higher level of math. Also, a box plot can be drawn from a cumulative frequency curve.

Comments

Submit a Comment

  • Reynold Jay profile image

    Reynold Jay 

    6 years ago from Saginaw, Michigan

    Heck--I understood this?!?! a miracle!! A box does set it up for me. I found I enjoyed this very much. You have this laid out beautifully and it is easy to understand. Keep up the great HUBS. I must give this an “Up ONE and awesome.” I'm always your fan! RJ

    Based upon your HUB, you might enjoy this HUB about quantum physics that few others would under stand…

    https://hubpages.com/education/Ben-takes-a-Quantum...

working

This website uses cookies

As a user in the EEA, your approval is needed on a few things. To provide a better website experience, hubpages.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: https://hubpages.com/privacy-policy#gdpr

Show Details
Necessary
HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
LoginThis is necessary to sign in to the HubPages Service.
Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
AkismetThis is used to detect comment spam. (Privacy Policy)
HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
Features
Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
MavenThis supports the Maven widget and search functionality. (Privacy Policy)
Marketing
Google AdSenseThis is an ad network. (Privacy Policy)
Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
Index ExchangeThis is an ad network. (Privacy Policy)
SovrnThis is an ad network. (Privacy Policy)
Facebook AdsThis is an ad network. (Privacy Policy)
Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
AppNexusThis is an ad network. (Privacy Policy)
OpenxThis is an ad network. (Privacy Policy)
Rubicon ProjectThis is an ad network. (Privacy Policy)
TripleLiftThis is an ad network. (Privacy Policy)
Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
Statistics
Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)