Bimodal Histogram- Open Middle Problem

Directions: Using the integers 1 to 9, create a data list that produces the following graph.  (You may use an integer more than once)

Bimodal-histogram.png

What do you notice about the graph?  How does that help you with the problem?

Justify why your list works.

Are there any other data lists that produce the same graph?  Provide an example.

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Box Plots- Open Middle Problem

Directions: Using the integers 0 to 9, create a data set that will produce the following Box Plot.  You may use the numbers more than once.

boxplot.png

 

What is the least amount of points you need to create the graph?

What is the greatest amount of points you need to create the graph?

Can you have the same amount of points but different values?  (Could 1,1,3,3,5,5,7,7,9,9 product the same box plot as 1,1,3,4,5,5,6,7,9,9?) If so, provide an example.

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?