STATISTICS 101 - Homework 2
Due Friday, February 1, 2002
• Homework is due by 5:00 PM on the due date at your course instructor’s office. You can always hand
in your homework at the end of lecture on Friday.
• You may talk with others about the homework problems but please write your solutions up independently.
• Please answer homework questions in complete sentences. Make sure to staple the pages of your
assignment together. Be sure to indicate your lab section letter on your paper.
Homework with out the correct lab section will marked as late.
• You normally will have an opportunity to get help on homework during lab.
Reading:
Jan. 21
Jan. 28
- Jan. 25
- Feb. 1
Section 1.2
Sections 2.1, 2.2
Assignment:
1. Read pages 32-42 of the text and do problems 1.32, 1.36, 1.42, and 1.46.
2. On homework 1 the birth weights of 44 babies born at a Brisbane, Australia hospital were given.
Eighteen of those babies were girls. Their birth weights, in grams, are given below.
3837
3523
2383
3334
3430
3500
2208
3480
3866
2576
3116
3542
3208
3428
3278
3746
2184
1745
(a) Calculate the mean and median for these data. Comparing these two values, would you say the
distribution of weights is skewed left, symmetric, or skewed right? Explain briefly your choice.
(b) Calculate a five number summary for these data and use this to construct a box plot. Be sure
to include a realistic axis for the box plot. Is the distribution of scores symmetric or skewed?
Explain briefly what it is about the shape of this box plot that indicates symmetry or skew.
(c) What are the values of the range and the InterQuartile Range (IQR) for these data?
(d) Suppose the hospital found out that the scale was not calibrated correctly and each of the reported
weights above is 200 grams more than it should be. If we correct for this mistake how would the
mean, median, range and IQR change? Hint: Don’t change the data and recalculate
the answers. Instead, think about what each measures and how that is affected by
subtracting a constant.)
3. Below are the heights (inches) of ten female students chosen at random from those currently enrolled
in Stat 101.
67, 65, 69, 64, 63, 65, 64, 66, 66, 71
(a) Calculate the sample median and sample mean for these data. Interpret each of these values
within the context of the problem. That is, what does the median (mean) tell you about the
height of females in Stat 101? What does the comparison of these values tell you about the skew
or symmetry of the distribution of female heights?
(b) Compute the standard deviation for these data using the definitional formula: (pg. 38 in the text)
s P
(X − X̄)2
s=
n−1
1
(c) Check your answer in (e) by using one of the following.
• the computational formula given below
v
P
u
u P 2 ( X)2
u
X −
n
t
s=
n−1
• a calculator with statistics capabilities
• a computer program that calculates standard deviation.
4. (JMP assignment) How faithful is the Old Faithful Geyser in Yellowstone National Park? In the table
below are the times (minutes) between eruptions of the Old Faithful Geyser during part of August
1985.
80
81
84
74
93
80
108
62
81
51
71
50
54
85
54
60
50
79
74
82
57
89
85
75
86
92
77
54
59
58
80
54
58
65
53
43
57
80
81
81
75
90
79
76
78
89
80
73
66
49
77
73
57
58
52
60
61
81
87
92
60
60
88
91
83
84
82
62
53
50
86
83
68
50
60
69
48
81
80
88
77
65
76
87
87
74
81
71
50
62
56
82
78
48
49
71
73
79
87
93
(a) Go to the webpage www.public.iastate.edu/∼wrstephe/stat101.html. There is is a link for
Old Faithful Data for Homework 2. Click on the right mouse button and select Save Link
As. Save this file as geyser.txt on either the computer’s hard drive, or on a diskette.
(b) Start the JMP program and select File → Open from the JMP menu. Enter the name of the
file (geyser.txt), and change the Files of type: settings to Text Import Preview. Then click
on Open and then Delimited. In the box that appears, click on Space in the End of Field
Box. Put a check mark in the box near Table contains column headers. Click on Apply
Settings. At this point, JMP gives you a preview of the column names and the first two rows of
your data. If everything looks good, press OK.
(c) We want to describe the distribution of this data. Select Analyze → Distribution from the
JMP menu. Select the column Times and click the button Y, Columns. Then click on OK.
(d) You should now have a histogram, boxplot, and statistics for this data set. We want to make
a few changes to the information JMP has calculated. First, click on the red triangle next to
Times and select Stem and Leaf. This should add a stem-and-leaf plot to your window. Now,
click on the red triangle next to Times and select Histogram Options → Count Axis. This
should add a count axis to the histogram in the window. Again, click on the red triangle next
to Times and select Display Options → Horizontal Layout.
(e) From the JMP Menu, select File → Print to print your output. Turn this in with your assignment.
Using this output, answer the following questions on a separate piece of paper.
i. What percentage of the times between eruptions are less than one hour? greater than an
hour and a half?
ii. Describe the shape of this distribution. Based on your answer, would you expect the mean
to be equal to, less than, or greater than the median? Explain your answer.
iii. Give the five number summary for these data.
iv. Give the mean and standard deviation for these data.
v. Did JMP split the stems in the stem plot? If yes, how did JMP split the stems? If no, do
you think JMP should have split the stems?
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