# Data and Standard Deviation2- Open Middle Problem

So my local Probability and Statistics guru (@veganmathbeagle) sent me a problem she encountered in a textbook that was very Open Middle-ish.  I modified it a bit and here it is…

Directions: Using the numbers 1 to 9, using each only once, create a data set of 4 numbers that fit the following criteria:

The four numbers have the smallest possible standard deviation:

___ , ___ , ___ , ___

The four numbers have the largest possible standard deviation:

___ , ___ , ___ , ___

1. Is there more than one data set for either question?  If so, what is it?
2. How would allowing the use of repeat numbers effect the standard deviation?
3. What would your data sets look like if this was allowed?

## 3 thoughts on “Data and Standard Deviation2- Open Middle Problem”

1. Thanks for sharing this tweak! I love it! That is my goal and thank you for reminding me and inspiring me to take what we’ve got and tweak it!

2. Thanks Amy! If you want help “refitting” some of your problems into Open Middle problems, feel free to contact me. I’m also more than willing to help you through the process so you can create your own great materials.

• Eu nÃ£o consegui resistir e esperar a legenda em portuguÃªs. Mesmo com meu ingles limitado, usei a legenda nesta lingua. Muito embora muitas passagens dos diÃ¡logos tenham sido nebulosas, devo dizer: roteiro estupendo, atores fantÃ¡sticos, foÃ-srafiaoedit§Ã£o-sonoplagtia primorosas, tudo Ã© um brilhante exercÃ­cio de direÃ§Ã£o. Espero que a esperiÃªncia de assistir este episÃ³dio duplo aconteÃ§a por muitas e muitas temporadas.