2- Way Frequency Table- Open Middle Problem

Directions: Using the digits 1 to 9, at most once each, fill in the boxes in this two way frequency table to make the statements true.

capture1.jpg

 

1. Students were four times as likely to wear low athletic shoes than high casual shoes

2. Three-sevenths of the students who wear low shoes wear casual ones.

3. More students wore athletic high tops than casual shoes

 

Other Questions:

How many students were surveyed?

Can you find the probability that a student is wearing any of the shoe choices?

What does this data tell you?

 

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?

 

Data and Standard Deviation- Open Middle Problem

Directions: Using the numbers 1 to 9, using each only once, create a data set of 5 numbers that fit the following criteria:

Mean = 5

Standard Deviation = 2.6

___ , ___ , ___ , ___ , ___

 

  1. Create a data set with the same mean but a smaller standard deviation
  2. Create a data set with the same mean but a larger standard deviation
  3. Explain why your standard deviation changes but your mean remains the same
  4. Explain what changes would happen if this is a sample of the population
  5. What would happen to your mean and standard deviation if you added 20 to each of your initial data points?