Key to homework 1, STAT2331, Fall 2005

1) (1.8) A stemplot is as follows

10 | 1 3 9
11 | 5
12 | 6 6 9
13 | 7 7
14 | 0 8
15 | 2 4 4
16 | 5 5
17 | 8
18 |
19 |
20 | 0

I would say that the 200 is an outlier. The center is about 137-140. The range, ignoring the outlier is from 101 to 178.

2) (1.25) + 3) (1.26) Below is a back to back stemplot of Ruth's and McGwire's home run total

      9 9 | 0 |
            | 1 |
         2 | 2 | 2 5
9 9 3 2 | 3 | 4 5
      9 2 | 4 | 1 6 6 6 7 9
      8 2 | 5 | 4 4 9
            | 6 | 0
         0 | 7 |

As required, Ruth's numbers are on the right, McGwire's on the left. Now we'll answer the specific questions;

1.25: Symmetry? Ruth's numbers look roughly symmetrical to me.
         How many homers in a typical year? The center of Ruth's distribution is in the upper 40's, about 46.
         Is 60 an outlier? Doesn't look like it.

1.26: First we'll answer the same questions for McGwire.
    Symmetry? No obvious asymmetry.
    Typical year? Probably about 40.
    Is 70 an outlier? It looks like it is. Also the two 9's seem to be outliers. For the low scores we have an explanation, but for the high score we don't have a clear one.

So the main points of comparison with Ruth seem to be that McGwire's "typical" output was lower, but his output of homers was also more variable than Ruth's.

4) (2.3) Generally we expect house prices to be right-skewed, so the mean will be greater than the median, hence it will be $210,900. The median would then be $163,900. 

5) (2.4) With the excellent 73 HR season, Bonds mean and median are 36.1 and 34 homers respectively. Without the 73-HR year the mean and median are 33.8 and 34. This illustrates that the median is not affected by the removal of extreme observations (which could possibly be classified as outliers).