Stat 2000, Homework 3, Question 3 - Solution

• 1) Summary Statistics:
  
  Below are the summary statistics for wins and payroll. The numbers listed here match those calculations we did in class. Note that this is the sample standard deviation.
  
  
  Summary statistics

  Variable	n	Mean	Variance	Std. Dev.	Median	Range	Min	Max	Q1	Q3
  wins	30	18.833334	19.591953	4.42628	19	21	8	29	16	21
  payroll	30	40.233334	224.87471	14.995823	41	60	9	69	31	52

  
  
  
  
• 2) Histograms:
  
  For 30 observations, we would expect about 5 to 6 (or perhaps up to 7) different classes. The histogram for wins only has 3 classes. The histogram for payroll is OK.
  WebStat allows us to modify starting point and class width. Here is a better histogram for wins with 5 classes (where the selected starting point is 0 and the class width is 5).
  
• 3) Stem-and-Leaf:
  
  The stem-and-leaf plot for payroll looks as expected. But why the `Low' amd `High' in the stem-and-leaf plot for wins?
  
  

  Variable: wins
  Low : 8.0
  1 : 144
  1 : 55666778999999
  2 : 0000124444
  2 : 6
  High: 29.0
  

  
  

  Variable: payroll
  0 : 9
  1 : 3
  2 : 02356
  3 : 1233479
  4 : 1157899
  5 : 022356
  6 : 039
  

• 4) Boxplot:
  
  The boxplots for this data set look OK. But some warning - WebStat does not produce the modified version of the boxplot we introduced in class, i.e., outliers are not labeled with a `*' symbol. The lines outside the box really stretch to the min and to the max - no matter whether these are below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR. Check yourself by adding some small or large value (e.g., -500 or 500) to the data set.