Description
Now that you have completed all of the statistical calculations involved with your analysis of the survey, it is time to put the project together. Your final project submission will be a single document that contains information from all of the previous components along with your written analysis and comments on the survey results.
The format for your final project submission should include the following sections, in this order:
Title Page.
Executive Summary (2–3 double-spaced pages): This should be a summary of the findings and conclusions of the study you developed and conducted. Discuss each of your six survey questions.
Reflection Statement (1–2 double-spaced pages): This needs to include what you learned both in the course and in this project. Review the competencies of this course as well as the criteria of this project to make sure you are focusing on the correct concepts for your reflections.
Appendix (This includes your supporting data):
Introduction.
Data Collection Plan.
Descriptive Results.
Inferential Statistics.
Table of Data From the Survey Data Generator.
The two sections that are new for this project component are the executive summary and the reflection statement. You may also need to edit your introduction to make it fit the style of a project document. The remaining items should be treated as an appendix. As you write your executive summary, you may wish to refer the reader to particular graphs or results in this supporting data section.
Make sure you have watched the Week 10 Project Video. Your instructor walk you through the process for completing this assignment.
Executive Summary
Write a summary (2–3 double-spaced pages) of your course project for someone interested in your work. While you did a lot of calculations and quantitative analysis in the project, your executive summary should give the reader a quick summary of your survey intent, design, and results without an overload of numbers and formulas. Discuss each of your six survey questions.
Focus on communicating the results and interpretations of your results. You will not be able to comment on every little finding, so you will have to make some judgments about what might be the most interesting or revealing results.
Discuss inferential statistics and how your survey data can be used to estimate or test population parameters such as the population mean and population proportion.
Write your executive summary professionally and with good writing practices.
Reflection Statement
Write a summary (1–2 double-spaced pages) of your thoughts on how your view of statistics has changed since you started this course and this project. We have covered a wide range of topics in this course, and many learners quickly forget the formulas they worked so hard to memorize.
While you may not remember the mathematical formulas, what concepts or ideas will you take from this course?
How will those ideas influence or impact your personal or professional life?
After you have written and integrated all of the previously described sections and items, refer to the Statistical Analysis course project description and then submit your project in the assignment area.
Competencies Measured
By successfully completing this assignment , you will demonstrate your proficiency in the following course competencies and rubric criteria:
Competency 2: Evaluate the adequacy of data collection methods.
Summarize survey intent and design.
Evaluate the adequacy of data collection methods.
Derive logical conclusions for inferential statistical calculations.
Competency 4: Solve problems in your personal and professional life by applying statistical procedures. Summarize survey results.
Interpret survey results.
Reflect on what was learned from this project and from this course.
View Rubric
Unformatted Attachment Preview
Blank row, Table 1 begins in A8.
Blank row, Table 1 begins in A8.
Statistical Summary: Questions 1–4
Confidence Intervals: Questions 1–4
Sample
Sample
Question
Proportion
Size
#1
0.56
30
#2
0.43
30
#3
0.48
30
#4
0.44
30
End of Table 1, blank row. Table 2 begins in F8.
Question
Error
Lower Limit
Upper Limit
#1
0.181254885 0.378745115
0.741254885
#2
0.180776105 0.249223895
0.610776105
#3
0.182428068 0.297571932
0.662428068
#4
0.181254885 0.258745115
0.621254885
End of Table 2, blank row. Table 3 begins in A15.
Statistical Summary: Questions 5–6
Confidence Intervals: Questions 5–6
Sample Std Sample
Question Sample Mean
Dev
Size
#5
35.26666667 18.6934127
30
#6
80332.4 138515.221
30
End of Table 3, blank row. Table 4 begins in F15.
Blank row. Table 4 begins in F15.
Table 5 begins in F21.
Question
Error
Lower Limit
#5
6.825869206 28.44079746
#6
50578.60745 29753.79255
End of table, blank row. Table 5 begins in F21.
End of table, blank row. Table 5 begins in F21.
Upper Limit
42.09253587
130911.0075
Hypothesis Tests: Questions 1–6
Question
Ho
#1
p ≥ 0.55
#2
p ≤ 0.50
#3
p = 0.60
#4
p ≥ 0.75
#5
μ = 17
#6
μ ≤ 119
End of table, blank row.
Ha
p < 0.55
p > 0.50
p ≠ 0.60
p < 0.75
μ ≠ 17
μ > 119
Reject Ho When
z < -1.645
z > 1.645
z < -1.96 or z > 1.96
z < -1.645
z < -1.96 or z > 1.96
z > 1.645
Rejection criteria:
Left-tailed test (one-sided), reject Ho when z < -1.645.
Right-tailed test (one-sided), reject Ho when z > 1.645.
Two-tailed test (two-sided), reject Ho when z < -1.96 or z > 1.96.
End of worksheet.
Conclusion
We are 95% confident the true population proportion is between 0.293 and 0.547
We are 95% confident the true population proportion is between 0.604 and 0.836.
We are 95% confident the true population proportion is between 0.453 and 0.707.
We are 95% confident the true population proportion is between 0.527 and 0.773.
Conclusion
We are 95% confident the true population mean is between 14.72 and 15.92.
We are 95% confident the true population mean is between 118.17 and 123.95.
Test Statistic
Decision
0.110096377 Reject Ho
-0.766811581 Reject Ho
-1.341640786 Do not Reject Ho
-3.921224299 Reject Ho
5.352187718 Reject Ho
3.171831098 Do not Reject Ho
Summary
There is sufficient statistical evidence to show the population proportion is less than 0.55.
There is sufficient statistical evidence to show the population proportion is greater than 0.50.
There is not sufficient statistical evidence to show the populaton proportion is not 0.60.
There is sufficient statistical evidence to show the population proportion is less than 0.75.
There is sufficient statistical evidence to show the population mean is not 17.
There is not sufficient statistical evidence to show the population mean is greater than 119.
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257751
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50043
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127983
215152
124033
616575
207476
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56457
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Sample Size
Sample Proportion of each response:
1
0
Pie Charts
Proportion of Responses Q1
Sample mean
Sample median
Sample mode
Sample range
Sample standard deviation
Sample minimum
Sample maximum
Histogram
Bins
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
EXAMPLE (Part 1):
Here is my data exactly how it appeared in the original spreadsheet I
downloaded.
Each row represents one survey respondent (person), and each column
represents one question.
You must save a copy of your data EXACTLY LIKE THIS so that you
can tie together your responses for analysis. In other words, you must
know how EACH respondent answered for all six questions, by looking at
each ROW, so that you can draw conclusions and discuss your results
(this will be done in Weeks 9 and 10).
Refer to the corresponding assignment scoring guide for how your assignment will be scored.
PART 1
Question 1
Question 2
30
30
50.0000%
50.0000%
56.6667%
43.3333%
of Responses Q1
Question 3 Question 4
30
30
56.6667%
43.3333%
43.3333%
56.6667%
Proportion of Responses Q2
Proportion of Response
1
1
2
2
PART 2
Q5 Histogram
Frequency
Question 5
Question 6
35.26666667
80332.4
28
0
18
0
65
616575
18.69341269 138515.2211
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41105
Bins Frequency
0
17
41105
1
82210
3
123315
0
164420
4
205525
0
246630
2
287735
1
328840
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369945
1
411050
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452155
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493260
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534365
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575470
0
616575
1
657680
0
Frequency
Frequency
616575
15
20
25
30
35
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45
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statistic
Q6 Histogram
Frequency
83
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0
Stat
Proportion of Responses Q3
5 Histogram
Proportion of Responses Q4
1
1
2
2
55
statistic
Q6 Histogram
Stat
60
65
70
75
80
85
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31449
50043
56457
74612
124033
127983
140920
150294
207476
215152
257751
357227
616575
EXAMPLE (part 2)
Here I have sorted my data from small
I have done this so that I can easily fin
To sort your data, follow these steps
1. Highlight the entire column (make s
2. Right click and select “sort” and the
3. Next, a pop up window will appear.
4. Do this for each of your six columns
5. You do NOT need to provide me wi
you will submit to me, please just inclu
MPLE (part 2):
have sorted my data from smallest to largest in each column.
done this so that I can easily find the mode/s. Reminder: a data set can have one mode, no mode, or multiple modes.
t your data, follow these steps:
hlight the entire column (make sure to not miss any values).
t click and select “sort” and then “sort smallest to largest.”
, a pop up window will appear. Select “continue with the current selection” and click “sort.”
his for each of your six columns to sort your results.
do NOT need to provide me with a copy of your unsorted data – this is for your use only. For the assignment that
ll submit to me, please just include your SORTED data.
or multiple modes.
e assignment that
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0.43
0.57
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0.57
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31449
50043
56457
74612
124033
127983
140920
150294
207476
215152
257751
357227
616575
EXAMPLE (part 3):
Now, with my sorted data,
You can follow this example to help you
The following elements must be present
1. Proportion values for each of your four b
2. Mean, median, mode, standard deviation
3. A bar graph or pie chart for each of your
4. A histogram for each of your continuous
5. Interesting findings presented in the form
To calculate the mean, median, standard de
click on the fx button at the top (it is near t
select each formula, you will be
sure to include all the values and not accid
Excel.
Hint: you can click on each of the cells to
use that formula too. Extra hint: YouTu
doesn’t quite “click” :
Mean = MEAN
Median = MEDIAN
Mode = MODE
Standard Deviation = STDEV
Min = MIN
Max = MAX
Range: =MAX-MIN
Note you will need to manually find the
Remember that there can be one mode,
35.27 80332.40 MEAN
28
0 MEDIAN
18
0 MODE
18.69 138515.2 STDEV
18
0 MIN
83
616575 MAX
65
616575 RANGE
Note that the min/max/range values
here represent the actual SAMPLE
data that I received, and may not
necessarily match to my min/max
values from Unit 3
0.5
0.5
18
18
18
18
18
18
18
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29
34
36
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41
47
49
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52
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71
76
83
0.57
0.43
“p” proportion
“q” proportion
Proportions:
“p” represents the proportion of “0” responses that you received.
“p” represents the proportion of “0” responses that you received.
“q” reprsents the proportion of “1” responses that you received.
To find “p”, divide the number of “0” responses by the number
of total responses. Round as necessary.
To find “q”, divide the number of “1” responses by the number
of total respones. Round as necessary.
Question 3
yes
no
How to create Pie Charts
Click on the white area of this pie chart I have created to the
right. You will see the data that I highlighted and
used to make the pie chart.
You must input this data for each of your binary questions and
highlight it with your mouse. Then, at the top of the screen,
select “Insert” and then “Pie.”
If you need extra help formatting your charts there are many
excellent and helpful tutorial videos on YouTube.
How to create Histograms
Histograms for
Class, creating the histograms will likely be the most challening part of the
Unit 7 project, but the following tutorial will make it a lot easier! 🙂
Question 5
First, what is a histogram? A histogram is a graphical representaton of
frequency distribution. It shows a simple and clear picture of how many
times values that fall within a certain range occur. Let’s say that one of
your continuous questions is: how old are you? An effective graphical
representation is to show how many people fall within a certain age
bracket. For this, we use the histogram.
Bin
18 – 30
31 – 43
44 – 56
57 – 69
70 – 83
Let’s focus on my 5th question (which is the first continous question),
which was, “how old are you?” My min value is 18 and my max value is
83. My range is 65.
Steps:
1. My first step is to divide the range into even “classes” (bins). In this
case I choose to divide my range into 5 classes of width 13. If you do not
have a number that is wholly divisible, round up to the next whole number.
have a number that is wholly divisible, round up to the next whole number.
2. Now, I will create a frequency distribution table. This table will show
how many values fall within the classes that I identified above. Follow
the black arrow to see the frequency distribution table. In the left column
you will need to enter your class min and max values exactly as shown
with the dash in between them. In the right column, count the number of
values from your data set that fall within each range, and enter that
number.
Question 6
Bin
3. Next, you must highlight both of the columns. To see what data has
been highlighted, just click on one of the histograms that I have created to
the right and you will see the highlight appear around the data.
4. Once you have done this, click the “Insert” button at the top:
Interesting find
5. Next click on “Column” and then select the first 2D option:
Beliefs of those with
yes
no
6. Now, a bar graph will appear. But remember that the bars must have
NO GAPS between each other in order for it to be a histogram. The way
to do this is:
to do this is:
7. Right-click one of the bars and select “format data series.”
Interesting Findin
8. Next, slide the cursor to the “no gap” side.
9. Finally, you can add a title to your Histogram, as well as titles for the
horizontal and vertical axes. In Excel 2007, you can do this by clicking on
the histogram itself and then selecting the layout tab from the ribbon. You
will see many options that you can experiment with to format your graph.
I was interested to
people’s beliefs ab
findings” table and
Bachelor’s degree
41% of the people
GMOs are dangero
noticeable and wor
information on the
GMOs are not dan
the two groups out
consideration that
naturally curious a
Additionally, colle
provides for a grea
not be as true in a
speculations and a
on the topic to pro
will see many options that you can experiment with to format your graph.
10. Reminder about histograms. Remember – the important thing to think
about when creating your histogram is that it is a CLEAR and
EFFECTIVE visual. So, let’s say that you have only 5 possible values
for one of your continuous questions. In this case, it is OK for each
BAR to represent only ONE value because there are only 5 values and
the graph will not be cluttered. However, let’s say that you have a
range of 200 possible values as the answer. In this case, each BAR
must represent a RANGE of values, otherwise the graph will be too
cluttered if you have 200 bars.
Example of inappropriate histogram:
Why is this histogram inappropriate and ineffective? As you can see, the
range of values is quite large, from 23 to 99, so it is not a a good idea to
have one bar per each value. The graph is busy, cluttered, and not easy to
decipher. In this instance, it would have been much better for each bar to
represent a RANGE of values.
LE (part 3): Remember—scroll ALL the way DOWN this document, AND all the way to the RIGHT.
h my sorted data, I can proceed to analysis using descriptive statistics.
follow this example to help you complete the assignment. On the next tab you will find the REQUIRED template.
owing elements must be present in your submission:
tion values for each of your four binary questions.
median, mode, standard deviation, range, minimum, maximum for your two continuous questions.
graph or pie chart for each of your binary questions (4 total graphs).
ogram for each of your continuous questions (2 total graphs).
ting findings presented in the form of a table AND a graph.
ate the mean, median, standard deviation, range, min, and max, you should use Excel formulas.To use Excel formulas,
he fx button at the top (it is near the top where you type. Then, select the “Statistical” Category for formulas. When you
ch formula, you will be prompted to highlight the range values – simply highlight one question (column) at a time, and be
the values and not accidentally miss one. Below, I have listed the names/abbreviations of all the formulas in
u can click on each of the cells to the left to see the formula that I used when calculating the values – you should
formula too. Extra hint: YouTube has thousands of Excel tutorials – feel free to search for extra help if something
quite “click” 🙂
= MEDIAN
Deviation = STDEV
MIN
u will need to manually find the mode. The mode is the value that occurs most frequently in the data set.
ber that there can be one mode, multiple modes, or no mode.
Pie Charts for Binary Questions
Question 1
Male
Female
Question 2
15
15
yes
no
Do you hold at least a Bachelor’s
degree?
Are you male or female?
15
15
13
17
Male
Female
yes
13
no
15
15
13
Female
17
Question 3
Question 4
yes
no
13
17
yes
no
Do you believe that GMOs are
dangerous?
17
13
Could you provide a summary of how GMOs
are created and what risks have been found?
yes
13
yes
13
no
17
no
17
Histograms for Continuous Questions
Frequency
17
4
6
0
3
Here I just
manually
counted how
many values
fall within
the “bins”
(classes” I
identified.
Frequency
Question 5
Bin
18 – 30
31 – 43
44 – 56
57 – 69
70 – 83
no
Age Histogram
18
16
14
12
10
8
6
4
2
0
18 – 30
31 – 43
44 – 56
Age Range
57 – 69
70 – 83
identified.
Question 6
Frequency
0-100,000
100,001-199,999
200,000-299,999
300,000-399,999
400,000-499,999
500,000-616,575
21
4
3
1
0
1
25
20
Frequency
Bin
Income Histogram
15
10
5
0
Income Range
Interesting findings in the form of a table
How did I make this table? I just
manually counted how many peop
fall in each of the categories I crea
and manually entered these values
Excel. There is no “function” in Exc
to automatically create this table.
Interesting findings in the form of a graph
Beliefs of those with BS/BA or higher
yes
6
no
7
BS/BA or higher
Beliefs of those without BS/BA
yes
7
no
10
No BS/BA
IMPORTANT NOTE:
original graphs for the interesting
findings section, rather than just pasting
were already created in part 1 above.
6
7
7
yes
no
Do you believe that GMOs are dangerous?
yes
no
10
Do you believe that GMOs are dangerous?
Interesting Findings Explained:
I was interested to know if having a college degree would be related to
people’s beliefs about the dangers of GMOs. As my “interesting
findings” table and graphs above show, 46% of the people who hold a
Bachelor’s degree or higher believe that GMOs are dangerous, whereas
41% of the people who do not hold a Bachelor’s degree believe that
GMOs are dangerous. This is not a profound difference, but it is still
noticeable and worth mentioning. It is my belief that lack of
information on the subject of GMOs leads people to falsely believe that
GMOs are not dangerous. I speculate that the difference in beliefs in
the two groups outlined above might be accounted for by the
consideration that people who obtain a BS/BA or higher might be more
naturally curious and seek out information on various topics.
Additionally, college is a social and intellecutal community that
provides for a greater exposure to ideas and information, which might
not be as true in a non-college environment. However, these are just my
speculations and a lot of further research would need to be carried out
on the topic to provide any conclusive results.
RED template.
cel formulas,
ulas. When you
at a time, and be
formulas in
you should
p if something
How did I make this table? I just
manually counted how many people
all in each of the categories I created
and manually entered these values in
Excel. There is no “function” in Excel
o automatically create this table.
NOTE: Please create new/
al graphs for the interesting
gs section, rather than just pasting graphs that
already created in part 1 above.
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1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
29
0
1
34
31449
1
36
50043Sample Size
Sample
1
Proportion
36
56457
of each response:
1
41
74612
1
1
47
124033
0
1
49
127983
1
49
140920
1
1
1
1
52
150294
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
54
56
71
76
83
207476
215152
257751
357227
616575
This Template is
shift cells and rows up or down a
format of your submission must a
You must place your SORTED
(smallest to largest) data here.
You can delete this text box and the
arrow and then use as many rows as
necessary to place all of your data
towards the left.
30
35.26667 80332.4 Sample mean
28
0 Sample median
18
0 Sample mode
65
616575 Sample range
18.69341 138515.2 Sample standard deviation
18
0 Sample minimum
83
616575 Sample maximum
0.5 0.566667 0.566667 0.433333
0.5 0.433333 0.433333 0.566667
30
Helpful hint: Suppose your project is looking very good, but
you forgot to include a portion and need to clear some space
and insert some information. Simply highlight an entire row
of cells, right click, then “insert” and “shift cells down” (or to
any other direction). You can press “control + y” to repeat the
action (shift the cells again to clear more space) or “control +
z” to undo the action.
Histograms for
Question 5
Question 6
Bins
0
41105
82210
123315
164420
205525
246630
287735
328840
369945
411050
452155
493260
534365
575470
616575
657680
Interesting findi
Question 2
0 (Dissatisfied)
0 (Dissatisfied)
1 (Satisfied)
1 (Satisfied)
Interesting findi
Interesting Find
Template is required. You must place all of your work as outlined below. Note: You are welcome to
ells and rows up or down and left or right to accomodate any need for extra space. However, the basic
t of your submission must adhere to this template.
Bonus hints to make your life easier 🙂
SORTED
data here.
1. Did you accidentally make a mistake? Delete something you didn’t mean to? Hit Control + z and
it will undo the last action. You can repeat this several times to delete multiple actions.
this text box and the
n use as many rows as
lace all of your data
2. Remember that you can easily resize graphs by clicking inside the graph and dragging the corner
3. To write inside Excel, click on “Insert” then “shapes” and then click the square
“A” in it, which will insert a text box like this one. You can expand the size by clicking inside the
text box and then dragging the corners.
30
30
Pie Charts for Binary Questions
Question 1
Sample Size
Question 2
30
30
Proportion of Responses
1 Q1 50.0000%
0
Proportion of Responses Q2
56.6667%
43.3333%
50.0000%
1
2
Question 3
Question 4
30
Proportion
of Responses
30
Q4
Proportion of Responses Q3
56.6667%
43.3333%
43.3333%
56.6667%
1
2
2
Histograms for Continuous Questions
0
9
3
5
1
2
1
3
2
1
0
0
1
1
1
Q5 Histogram
Frequency
Question 5
Bins Frequency
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
10
9
8
7
6
5
4
3
2
1
0
15
20
25
30
35
40
Q6 Histogram
Frequency
17
1
3
0
4
0
2
1
0
1
0
0
0
0
0
1
0
50
statistic
Question 6
Bins Frequency
0
41105
82210
123315
164420
205525
246630
287735
328840
369945
411050
452155
493260
534365
575470
616575
657680
45
18
16
14
12
10
8
6
4
2
0
Stat
55
Interesting findings in the form of a table
Question 2
0 (Dissatisfied)
0 (Dissatisfied)
1 (Satisfied)
1 (Satisfied)
Question 3
0 (High School)
1 (College)
0 (High School)
1 (College)
Average Job Average
Satisfaction Education Level
2.5
0.7
2.5
0.8
4
0.6
4
0.9
Interesting findings in the form of a graph
Interesting Findings
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
1
2
Average Job Satisfaction
3
4
Average Education Level
Interesting Findings Explained:
The analysis reveals interesting insights into the relationship between job satisfaction, education level, and the binary respon
to Questions 2 and 3. Overall, respondents who reported being satisfied with their jobs tend to have higher average job
satisfaction levels compared to those who are dissatisfied. Additionally, individuals with a college education (Question 3 = 1)
generally report higher job satisfaction levels compared to those with only a high school education. These findings suggest a
potential correlation between education level and job satisfaction, highlighting the importance of education in career
satisfaction. However, it’s essential to interpret these findings cautiously, considering they are based on the provided sample
The analysis reveals interesting insights into the relationship between job satisfaction, education level, and the binary respon
to Questions 2 and 3. Overall, respondents who reported being satisfied with their jobs tend to have higher average job
satisfaction levels compared to those who are dissatisfied. Additionally, individuals with a college education (Question 3 = 1)
generally report higher job satisfaction levels compared to those with only a high school education. These findings suggest a
potential correlation between education level and job satisfaction, highlighting the importance of education in career
satisfaction. However, it’s essential to interpret these findings cautiously, considering they are based on the provided sample
data and may not generalize to the entire population.
are welcome to
owever, the basic
‘t mean to? Hit Control + z and
e multiple actions.
e graph and dragging the corners.
ck the square icon with the letter
the size by clicking inside the
ortion of Responses Q2
1
2
portion of Responses
Q4
1
2
2
stogram
55
60
65
70
75
80
85
on level, and the binary responses
o have higher average job
ege education (Question 3 = 1)
ation. These findings suggest a
e of education in career
based on the provided sample
on level, and the binary responses
o have higher average job
ege education (Question 3 = 1)
ation. These findings suggest a
e of education in career
based on the provided sample
Q1
Q2
0
0
1
0
0
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
Q3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
Q4
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
Q5
0 NaN
0 NaN
0 NaN
1 NaN
0 NaN
1 NaN
1 NaN
1 NaN
0 NaN
1 NaN
0 NaN
1 NaN
0 NaN
0 NaN
0 NaN
0 NaN
1 NaN
0 NaN
0 NaN
0 NaN
0 NaN
0 NaN
0 NaN
1 NaN
0 NaN
1 NaN
0 NaN
0 NaN
0 NaN
1 NaN
1 NaN
0 NaN
1 NaN
1 NaN
0 NaN
0 NaN
0 NaN
0 NaN
1 NaN
0 NaN
0 NaN
Q6
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
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