Statistics Survey Project
Group Members:
Group Topic:
Deadlines:
March 4
Part One: Qualitative Data
March 18
Part Two: Quantitative Data
April 29
Part Three: Summary
TOPIC:
Part One: Qualitative Data
1
Part Two: Quantitative Data
Question Question
Number
Type
5
2
3
4
6
7
8
Question
Person
Responsible
Part One: Qualitative Data
Group Question
Member Number
Actual Question
1
2
3
4
1. Produce a Pareto chart for this data. Be sure to label each axis, give your chart a title, and make it easy for
the reader to understand your data. See Example A.
2. Produce a pie chart for this data. Be sure that each sector is clearly labeled with the number of responses,
the percent of responses, and the category that it represents. Give this graph a title. See Example B.
3. Complete a contingency table for this data compared to gender from the demographic questions. Divide
your data into TWO categories only. Complete the table with the actual counts AND the percentages in each
gender row. Write a short conclusion about whether you find an association with gender or an overall trend.
Describe that association or trend. See Examples C, D, and E.
4. Further investigate this question by producing a contingency table for EACH GRADE LEVEL, comparing your
question categories to gender again. FOR EACH GRADE LEVEL, Complete the table with the actual counts AND
the percentages in each gender row. Write a short conclusion about whether you find an association with
gender or an overall trend. Describe that association or trend.
5. Write a summary of what you have learned about DVHS students from the results of this question and your
analysis. Be specific, and refer to your visual displays to support your claims.
Qualitative Data Examples
What is your favorite type of vehicle?
Data:
Truck
car
Car
Jeep
Truck
SUV
car
SUV
Car
Car
Jeep
truck
SUV
SUV
Car
motorcycle
Truck
Motorcycle
Bicycle
skateboard
EXAMPLE A
Pareto Chart
Frequency Distribution:
Category
Truck
Car
Jeep
SUV
Motorcycle
Bicycle
skateboard
TOTAL
Tally
XXXX
XXXXX X
XX
XXXX
XX
X
X
Count
4
6
2
4
2
1
1
20
Percent
20
30
10
20
10
5
5
100
Favorite Type of Vehicle
35
30
30
PERCENT
25
20
20
20
15
10
10
10
5
5
5
0
Car
SUV
Truck
Jeep
TYPE OF VEHICLE
Motorcycle
Bicycle
Skateboard
EXAMPLE B
Pie Chart
Favorite Type of Vehicle
Skateboard, 1, 5%
Bicycle, 1, 5%
Motorcycle, 2, 10%
Car, 6, 30%
Jeep, 2, 10%
Truck, 4, 20%
SUV, 4, 20%
EXAMPLE C
Contingency Table
Male
Female
Motorized, 4 wheel
Vehicles
9=82%
7=78%
Other
TOTAL
2=18%
2=22%
11=100%
9=100%
This contingency table indicates that there is NOT an association between favorite type of
vehicle and gender. There is an overall trend that most students prefer motorized vehicles
with four wheels, regardless of gender. This is a strong trend.
EXAMPLE D
Contingency Table
Male
Female
Motorized, 4 wheel
Vehicles
2=18%
7=78%
Other
TOTAL
9=82%
2=22%
11=100%
9=100%
This contingency table indicates that there IS an association between favorite type of vehicle
and gender. Females are more likely to prefer motorized, four-wheel vehicles, and males are
more likely to prefer other types of vehicles. This is a strong association.
EXAMPLE E
Contingency Table
Male
Female
Motorized, 4 wheel
Vehicles
6=50%
4=50%
Other
TOTAL
6=50%
4=50%
12=100%
8=100%
This contingency table is inconclusive. It shows neither overall trend nor association with
gender.
Part Two: Quantitative Data
Group
Member
Question
Number
5
6
7
8
Actual Question
1. Enter the data into a calculator and run the 1-Variable Stats. Record the results. Label each value not only
with its symbol or abbreviation, but with its description. For example, S x=2.563, the standard deviation for
this sample. See Example F.
2. Using the statistics you found in step 1, produce a boxplot to represent this data. Be sure that your graph is
clearly labeled and easy for the reader to understand. See Example G.
3. Group your data into 4-6 reasonable intervals. It is required that those intervals be equal in size. Complete
a group frequency table for your data. Use that table to create a histogram to represent this data. Be sure
that your axes are labeled, that your graph has a title and is easy to read. See Example H.
4. Test your data for outliers. Be clear about which outlier test you are going to use, and show all the steps to
apply that test clearly. Make a definite conclusion about which data are outliers. How does this affect the
data? See Examples I, J, and K.
5. Perform an analysis of your data compared to the demographic information collected. Do that by
completing the four contingency tables described below. Divide your data into TWO reasonable categories,
and use those same categories in each contingency table. See Example L.
a)
b)
c)
d)
Gender (M, F) and your two categories
Grade level (non-seniors, seniors) and your two categories
Age (under 16, 16 and up) and your two categories
Employment (Job, No job) and your two categories
Complete each table with the actual counts AND the percentages in each demographic row. Write a short
conclusion about whether you find an association with the demographic information or an overall trend.
Describe that association or trend.
5. Write a summary of what you have learned about DVHS students from the results of this question and your
analysis. Be specific, and refer to your visual displays to support your claims.
Qualitative Data Examples
EXAMPLE F
1-Var Stats
Question: How many times have you stayed up late because of a homework assignment or
test, in the last two weeks?
Data:
3
4
0
1
1
0
1
1
Calculator Results
𝑥̅ = 2.06
𝑆𝑥 = 2.294
n = 16
minX = 0
𝑄1 = .5
Med = 1.5
𝑄3 = 3
MaxX = 9
0
4
3
2
9
2
2
0
Meaning?
The mean for this sample is 2.06 late nights. This is the average.
The standard deviation for this sample is 2.294 late nights. This
measures how spread out the data is.
The sample size is 16.
The minimum number of late nights was 0.
The first quartile for this data is 0.5. 25% of the data is below this value.
The median for this data is 1.5. 50% of the data is below this value.
The third quartile for this data is 3. 75% of the data is below this value.
The maximum number of late nights was 9.
EXAMPLE G
BoxPlot:
Made with http://www.imathas.com/stattools/boxplot.html
Times up late for schoolwork
EXAMPLE H
Grouped Frequency Table
Number of Late Nights
(interval notation)
Frequency
(0, 2]
(2, 4]
(4, 6]
(6, 8]
(8, 10]
11
4
0
0
1
Times up Late for Schoolwork
12
Number os students
10
8
6
4
2
0
2
4
6
Number of Late Nights
8
10
EXAMPLE I
Empirical Rule TEST for OUTLIERS
From our calculator work:
𝑥̅ = 2.06 and 𝑆𝑥 = 2.294
Lowest Expected Value = 𝑥̅ - 3𝑆𝑥 = 2.06 – 3(2.294) = -4.822
No data is lower than this, so there are no outliers on this end of the data.
Highest Expected Value = 𝑥̅ + 3𝑆𝑥 = 2.06 + 3(2.294) = 8.942
The data value of 9 is larger than this, so 9 is an outlier.
EXAMPLE J
IQR TEST for OUTLIERS
From our calculator work:
𝑄1 = .5
Med = 1.5
𝑄3 = 3
IQR ; 3 – 0.5 = 2.5
Lowest Expected Value = 𝑄1 − 1.5 (𝐼𝑄𝑅) = 0.5 − 1.5 (2.5) = −3.25
No data is lower than this, so there are no outliers on this end of the data.
Highest Expected Value = 𝑄3 + 1.5 (𝐼𝑄𝑅) = 3 + 1.5(2.5) = 6.75
The data value of 9 is larger than this, so 9 is an outlier.
EXAMPLE K
Z-SCORE TEST for OUTLIERS
𝑧=
𝑥−𝑥̅
𝑆𝑥
From calculator work: 𝑥̅ = 2.06 and 𝑆𝑥 = 2.294
Lowest Expected Value: z = - 3.
–3 =
𝑥−2.06
2.294
, so x = -4.822
No data is lower than this, so there are no outliers on this end of the data.
Highest Expected Value: z = 3.
𝑥−2.06
3 =
2.294
, so x = 8.942
The data value of 9 is larger than this, so 9 is an outlier.
EXAMPLE L
Contingency Table
Male
Female
Less than twice
6 = 86%
7 = 78%
Twice or more
1 = 14%
2 = 22%
TOTAL
7= 100%
9 = 100%
There is not an association with gender. There is a strong trend that most students have
stayed up late for schoolwork less than twice in the past two weeks.
Part Three: Summary
1. Complete the table shown. Each group member should complete the two rows that pertain
to their questions. Have your group edit your work and give feedback.
Question
Number
1
2
3
4
5
6
7
8
Actual Question
Summary of Our Analysis
Proposed Revisions to the
Question
2. Explain what recommendations you would make to DVHS administration based on your
survey data and analysis. Back these recommendations from your data. Be clear about what
changes you are asking for and why. Each group member should contribute at least one
recommendation. Be sure to indicate which contribution is from each member.
3. Discuss any potential lurking variables that may have influenced your data. What were
they? How could they have influenced your data? Do you think they were a major or a minor
influence? How could we measure them for next time?
4. Discuss any possible bias errors that may have influenced your results. What were they?
How could they have influenced your data? Do you think they were a major or a minor
influence? How could we change our process to avoid or at least minimize them for next
time?
5. What was your margin of error for this survey? How does that affect our analysis? How
could the margin of error be improved next time?
6. Discuss what you (personally) have learned from this project. Be specific.