Statistics 101 – Laboratory 2
In this assignment, we will take a closer look at some of the data collected as a part of Laboratory 1 on
the height of students in Stat 101 this semester. You should work on this assignment in groups of 3 to 5
students.
1. A random sample of 80 students was taken from all students who completed the survey in
Laboratory 1 last week. The JMP output of the distribution of the heights, in inches, for these
100 students is located on the handout for this lab. The handout includes a stem and leaf display
of the heights, a five number summary and sample statistics for the heights. Use the JMP output
to answer the following questions.
a) Use the stem and leaf display to determine how many students had a height of 68 inches.
What percent of all students had this forearm length?
b) Use the stem and leaf display to describe the shape (number of modes, symmetry or
skewness, and presence of outliers) of the distribution of heights for the sample of Stat 101
students this semester.
c) The stem and leaf display suggests the presence of two modes, around 65 inches and the
other around 70 inches. Why do you think these data would have two modes instead of just
one?
d) Give the mean and median values for the height of this sample of Stat 101 students this
semester. How do these values reinforce your answer to b) above?
e) Calculate the Range and IQR for the height of this sample of Stat 101 students this semester.
Which one of these measures of spread would you use for these data? Explain your answer.
f) Give the standard deviation for the height of this sample of Stat 101 students this semester.
The standard deviation measures the “average” distance heights are away from what value?
g) One student reported a height of 66 inches, while another student reported a height of 76
inches. Which student’s height contributes a larger value to the standard deviation, the
student with the height of 66 inches or the student with height of 76 inches? Explain your
answer.
2. Another variable collected during Laboratory 1 was the gender of the student. The JMP output
for the distribution of the height of females in the sample of Stat 101 students and the
distribution of the height of males in the sample of Stat 101 students are located on the handout
for this lab. For each distribution, the handout includes a histogram of the heights, five number
summary and sample statistics for the heights. Use the JMP output to answer the following
questions.
a) Compare the shapes of the distribution of heights for male and female students in the sample
by pointing out any similarities and differences in shape.
b) Compare the sample median height of females to the sample median height of males. Also
compare the sample mean height of females to the sample mean height of males. What do
these comparisons tell you about the differences or similarities in the centers of the two
distributions?
c) Compare the Range for the height of females to the Range for the height of males. Do the
same for the IQR and standard deviation. What do these summaries tell you about the
differences or similarities in the variation of heights for males and females?
d) After studying the two distributions, do you think heights for males in the sample of Stat 101
students this semester are generally higher than heights for females in the sample of Stat 101
students this semester? Support your answer with information from the two distributions.
e) If we looked at all Stat 101 students who completed the survey, do you think heights for
males will be generally higher than heights of females for all students in Stat 101 who
completed the survey? Explain your answer.
1
Summary of Heights of 80 Randomly Selected Stat 101 Students Spring 2010
Stem and Leaf
100.0%
75.0%
50.0%
25.0%
0.0%
Five Number Summary
maximum
quartile
median
quartile
minimum
79
72
68
65
60
Sample Statistics
Mean
68.3875
Std Dev
4.2878803
N
80
Gender=Male
Count
Gender=Female
100.0%
75.0%
50.0%
25.0%
0.0%
maximum
quartile
median
quartile
minimum
Mean
Std Dev
N
71
67.5
65
63
60
65.283784
2.8199206
37
100.0%
75.0%
50.0%
25.0%
0.0%
maximum
quartile
median
quartile
minimum
Mean
Std Dev
N
79
73
72
69
62
71.05814
3.4610233
43
2
Stat 101 Lab 2
Group Answer Sheet
Group Members:
_______________________________
______________________________
_______________________________
______________________________
1. Heights
a) Number of students with height = 68 inches? __________
Percentage of students with height = 68 inches? __________
b) Describe the shape.
c) Why do you think these data would have two modes instead of just one?
d) Mean = __________
Median = __________
How do these values reinforce your answer in b) above?
e) Range = __________
IQR = __________
Which one of these measures of spread would you use for these data? Explain your answer?
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f) Standard deviation = __________
The standard deviation measures the “average” distance heights are away from what value?
g) One student reported a height of 66 inches, while another student reported a height of 76 inches.
Which student’s height contributes a larger value to the standard deviation, the student with the
height of 66 inches or the student with height of 76 inches? Explain your answer.
2. Heights by Gender
a) Compare shapes.
b) Compare centers using sample medians and sample means.
c) Compare spreads using sample Ranges, sample IQRs and sample standard deviations.
d) After studying the two distributions, do you think heights for males in the sample of Stat 101
students this semester are generally higher than heights for females in the sample of Stat 101
students this semester? Support your answer with information from the two distributions.
e) If we looked at all Stat 101 students who completed the survey, do you think heights for males
will be generally higher than heights of females for all students in Stat 101 who completed the
survey? Explain your answer.
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