Statistics 101 – Homework 2
Due Friday, January 26, 2007
Homework is due on the due date at the end of the lecture.
Reading:
January 17 – January 22
January 24 – January 31
Chapter 5
Chapter 6
Assignment:
1. A random sample of 35 Division 1-A Football teams is selected and the points they score
during the first week of the 2006 season are recorded. The data are given below.
10
28
10
35
21
30
35
52
41
10
31
35
0
10
17
27
14
39
20
42
3
47
13
61
52
45
54
7
38
35
45
10
35
15
24
a) Answer the questions, Who? and What? for these data.
b) Make a stem-and-leaf display of the scores.
c) Using the stem-and-leaf display, describe the distribution of scores. Make sure you
mention the shape, center, spread and any outliers or other interesting characteristics
of the distribution.
d) Calculate the sample mean score.
e) Calculate the sample median score.
f) Calculate the five-number summary for these data.
g) Given the value
∑ ( y − y ) = 9,007.54, calculate the sample standard deviation for
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these data.
h) Which do you think provides a more informative summary of these data; a five
number summary or the sample mean and sample standard deviation? Briefly
explain your answer.
During the second week of the 2006 season the points scored by the 35 Division 1-A Football
teams was also recorded. On the next page is JMP output for the distribution of scores for the
second week.
i)
Describe the distribution of scores for the second week. Make sure you mention the
shape, center, spread and any outliers or other interesting characteristics of the
distribution.
j) Give the value of the sample mean score. Give the value of the sample median score.
What does the relationship between these two values indicate about the shape of the
distribution?
k) Give the value of the sample standard deviation of the scores.
l) Construct side-by-side box plots (use a common scale) and use these to compare the
distribution of the first week’s scores to the second week’s scores.
1
Division 1-A Football Scores (Second Week 2006 Season)
6
4
Count
8
2
0
10
20
30
40
50
60
Quantiles
maximum
quartile
median
quartile
minimum
Leaf
667
Count
3
55567
1
5578
344
5
1
4
3
001134444
57
00334
7
00
9
2
5
1
2
70
0|0 represents 0
Scores
100.0%
75.0%
50.0%
25.0%
0.0%
Stem
5
5
4
4
3
3
2
2
1
1
0
0
Moments
57.000
41.000
24.000
15.000
0.000
Mean
Std Dev
N
28.1
15.73
35
2. (JMP assignment) Data are obtained on the forced expiratory volume (FEV) of youths
in East Boston in the late 1970’s. Forced expiratory volume (FEV) is a measure of lung
capacity, in liters. The initial measurements in the 1970’s provide a baseline values to
study the impact of smoking on lung function. The data for this problem are a random
sample of 100 FEV values. The data are available on the course web page both as a JMP
(.JMP) file and a straight text (.TXT) file. Follow the directions in the JMP Guide to
download the file and create output. Make sure to print the output and turn it in with
your assignment. Use the output in answering the following questions.
a) Describe the shape of the distribution of FEV. Based on this description would
you expect the mean to be equal to, less than, or greater than the median? Briefly
explain your answer.
b) Looking at the histogram, are there any apparent outliers? If so, what are their
values?
c) Give the five-number summary for FEV.
d) Looking at the box plot, are there any apparent outliers? If so, what are their
values?
e) Calculate the sample range and sample IQR for these data.
f) Give the sample mean and sample standard deviation for these data.
g) Did JMP split the stems in the stem-and-leaf plot?
h) Look at the raw data in the JMP data table and look carefully at the stem-and-leaf
plot. What did JMP do to the data before constructing the stem-and-leaf plot?
2