School

University of Cincinnati, Main Campus **We aren't endorsed by this school

Course

ENED 3061

Subject

Statistics

Date

Sep 25, 2023

Type

Other

Pages

5

Uploaded by bhertrick on coursehero.com

1
ENED 3061 Probability & Statistics
HW 3: Descriptive Statistics 2 - p.
Spring 2023, Murphy
due by 8:00am on Thursday February 2
Note: This is an individual assignment. The work you submit must be your own. Your
submission of work for this assignment indicates your affirmation of the CEAS Honor Code
statement, which is provided verbatim below.
https://ceas.uc.edu/about/info-current-students/academic-action-criteria.html
College of Engineering and Applied Science
Honor Code
As students of the University of Cincinnati's College of Engineering and Applied Science, we
honor the high standards required by our future profession.
We pledge to uphold those high standards by practicing integrity within our classrooms, our
communities, and our careers.
We believe in honest representation of individual work and in fair advancement of academic
position; therefore, we refuse to partake in actions at the expense of our academic integrity.
We expect academic integrity from our peers who share the responsibilities of this code.
Our commitment to this pledge entitles us to trust from our peers, our instructors, and our
institution. We maintain the right and share the responsibility to report any unfair advantage
with anonymity and without retribution.
I hereby affirm that this is my own work in accordance with the Honor Code of the University of
Cincinnati College of Engineering and Applied Science.

2
ENED 3061 Probability & Statistics
HW 3: Descriptive Statistics 2 - p.
Spring 2023, Murphy
due by 8:00am on Thursday February 2
Some of the work needs to be done by hand. You may include pictures of your hand-written
work (make sure it's legible and well organized) or you may type your work and answers.
(1)
Show and/or explain enough work
that we can tell what you did. For full credit, you must
fill in all of the cells.
´
x
=
∑
i
=
1
n
x
i
n
=
159
+
170
+
173
+
175
+
177.8
+
178
+
180.3
+
182.9
+
187
+
188
+
195.6
11
=
178.7818
s
2
=
∑
i
=
1
n
(
x
i
−´
x
)
2
n
−
1
=
972.382
11
−
1
=
97.2382
I used the equations in the headers of the table to calculate the deviations from the mean (
x
i
−´
x
=
x
i
−
178.7818
) and squared those values to get the deviation squared
I summed my
x
i
−´
x
values to get the sum of deviations. Because I rounded my values to 4
decimal places, that is why my sum of deviations is not zero.
(a) By hand (using a calculator), complete the table below to calculate the mean and
standard deviation for the given data set.
x
i
=
Height
(
cm
)
x
i
−´
x
(deviation from the mean)
x
(
¿¿
i
−´
x
)
2
¿
(deviation squared)
159
-19.7818
391.3203
170
-8.7818
77.1203
173
-5.7818
33.4294
175
-3.7818
14.3021
177.8
-0.9818
0.9640
178
-0.7818
0.6112
180.3
1.5182
2.3040
182.9
4.1182
16.9594
187
8.2182
67.5385
188
9.2182
84.9749
195.6
16.8182
282.8512
(b) Why does "sum of
deviations" work out to be
0 (or close to 0)?
The sum of deviations is the sum of
x
i
values minus the sum of the
´
x
´
x

3
ENED 3061 Probability & Statistics
HW 3: Descriptive Statistics 2 - p.
Spring 2023, Murphy
due by 8:00am on Thursday February 2
mean
´
x
=
¿
178.7818
sum of deviations =
-0.0003
sum of (deviations)
2
=
972.382
variance
s
2
=
97.2382
standard deviation
s
=
9.8609
(2)
Show and/or explain enough work
that we can tell what you did.
A data set has the following 25 values for one of the variables (same data set that was used
for HW 2: Descriptive Statistics 1):
19
7 71 71 84 10 80 91 19 27 30 82 21 98 64 26 78 50 24 61 93 39 16 99 29
Complete the follow items. Include screenshots of your Minitab results.
(a) Use Minitab to construct a histogram of the data. Include a screenshot of your Minitab
output.
(b) Use Minitab to calculate the mean
´
x
and the standard deviation s. Include a
screenshot of your Minitab output.