Lab 1 Part 1 Notes

Comparison A (starting on p. 3)

Calculate the mean of group 2: 
n
2 = 5
Sx  = 250
2 = 250 / 5 = 50

Calculate the standard deviation of group 2:
SS2 = 1000
s22 = 1000 / 4 = 250
s2 = sqrt(250) = 15.8

Graphical and numerical comparison derive the same conclusions:  a) same central locations b) greater variability in group 1. 

Comparison B (p. 8)

Plot values on a common stem:

Group 1       Group 2
        0|9|
        0|8|
        0|7|0
        0|6|0
        0|5|0
         |4|0
         |3|0
         |2|
         |1|
        (x10)

Compare the central locations and spreads of the distributions:  Group 1 has higher central location; groups have same variability. 

Calculate the means and standard deviations of each distribution.

1 =  350 / 5 = 70   
s1 = sqrt(1000/4) = 15.8

2 = 250 / 5 = 50
s2 = sqrt(1000/4) = 15.8 

How do your numerical statistics complement your graphical analysis? Both the graphical analysis and summary statistics provide identical conclusions (i.e., higher central location in group 1; equal spread in the groups). EDA and summary statistics complement each other. Advantages of summary statistics include that they are  (a) quantitative, (b) precise, (c) concise, and (d) are needed for inferential calculations that usually follow EDA (i.e., confidence intervals and p values).

Comparison C (p. 9)

Draw side-by-side stemplot and discuss your findings.

Group 1       Group 2
        0|9|0
         |8|0
        0|7|0
         |6|0
        0|5|0
         |4|
        0|3|
         |2|
        0|1|
        (x10)

Group1 has lower central location and greater spread.

Then calculate the means and standard deviations of the distributions.

1 =  50                
s1 =  31.6

2 = 70
s2 = 15.8