9th Test - Statistics

1) Given this series of data values:  -5,   -2,   -2,   -1,   0,   4

What is the mean (or average)?         -6/6 = -1
What is the median?                          (-2 -1)/2 = -1.5
What is the mode (if there is one)?       -2  
What is the range?                           4 - (-5) = 9

2) About what percentage of the whole is the shaded slice in the following pie chart? _____17%_______
 
    I gave full credit for anything between 15% - 20%
    I only gave 1/2 credit if the student said 1/6, since I specifically asked for a percentage.
 

3) If I were to sketch a distribution of life expectancies in a certain country, I might draw something like the histogram below.  Sketch next to it what you think the distribution of heights is for all 5th grade students at pioneer would be.

    A normal (bell-curved or Gaussian) distribution with height on the x axis. The min should be around 3ft and the max around 6ft and the mean around 4.5 ft.


4) One of these plots was created by plotting 50 truly random points. Each point was determined by an (x, y) coordinate pair, where x and y were random in the same way that rolling a dice is random. Circle the plot that you think was created in this manner.   

     the first plot is the random data. Some may think it is not random because of the clumping of points. However this clumping is known as Poisson clumping and is a well-known phenomenon. The second plot is too evenly distributed. True random data is not so uniformly distributed. The final plot is too dense near the center.

5) Suppose you were one of 200 students who took a standardized test. You got only 40% of the problems correct, but you scored in the 90th percentile. How many students scored lower than you?  _____180____. How many scored higher? ______19_______

  Other answers were acceptable since it is conceivable that your score tied one or more other scores.

6) Create a sequence of 10 numbers for which the median value is much higher than the mean value.

   There are many possible answers for this one. I gave 1/2 credit if your series had the median larger than the mean - even if it was only be a small amount. Here is one example of such a series:
    -1000, -1000, -1000, -1000,  1000, 1000, 1000, 1000, 1000, 1000
  median = 1,000
    mean =   200

7)  Given the following histogram representing a distribution of test scores, estimate the mean and median scores.   mean:______28______       median:____24______

Full credit for  mean: 26-30       median:  23-25
No one got full credit for this one. A few got half credit.