Chapter 14 - Standard Deviation Exercises

Standard Deviation: A measure of dispersion around the mean, calculated so that approximately

• 68 percent of the cases will lie within plus or minus one standard deviation (SD) from the mean,
• 95 percent will lie within plus or minus 2 SDs, and 
• 99.9 percent will lie within 3 SDs.

A group of hungry, hungry hippo bulls has an average weight of 4000 lbs with a standard deviation of 200 lbs. The weights follow the normal curve closely.

1. Is weight a continuous or discrete variable?

2. A runt hippo bull, weighing 1 SD below the mean, challenges the alpha hippo bull, weighing 1 SD above, for mating privileges.
a) What is the difference in their weight?
b) Approximately what percentage of this hippo bull group weigh more than the runt, but less than the alpha?


(Click "Read more..." for the answers!)

1. Weight is a continuous variable. It can be broken down into an infinitely small number of fractions.
     Ex. 120.000, 120.001, 120.002....121.000, etc.
   
     An example of a discrete variable would be the number of siblings you have. You can have 4 siblings, but not 3.5 siblings (even if you chop one of them in half).

2. a) The average is 4000 lbs and the SD is 200 lbs.
        One SD below the average would be 4000 - 200 lbs = 3800 lbs = Runt Hippo's weight.
       One SD above the average would be 4000 + 200 lbs = 4200 lbs = Alpha Hippo's weight.
                                                                  The difference: 400 lbs

     b) Sixty-eight percent of the hippo bulls will weigh between one SD below and one SD above the mean (because entropy and normal curve distributions are magically cool like that).