1. Statistics Project
By Ella Hill 1*

2. Section 1
Survey Questions and Data

3. Survey Questions Population: GT 8th Graders
Quantitative Question: How many times, if any, did you go out of state this summer?
Characteristic Question: Do you wear glasses/ contacts or not?
Categorical Question: After school would you rather eat toast, apples, oranges, carrots, cookie, cereal, or nothing for a snack afterschool?

4. Survey data Amelia B. Yes 8 Cookie Tyler K. 6 Cereal Nicole B. No 2ID
*GT 8th Graders
Glasses/
Contacts or Not
Times Out of State
Snack Afterschool
Amelia B.
Yes 8
Cookie
Tyler K. 6
Cereal
Nicole B. No 2
Carson E.
Sierra H. 1
Carson S.
Nothing
Cristina S.
Apple
Christian W.
Carrots
Shea S.
Mason M.
Kyla L. 5
Oranges
Gavin H.
Apples
Anna C. 7
Owen S.
Kendall E.
Mekhi W.
Hayley F.
Owen W.
Nevaeh B.
Jakob K.
Tylee K.
Drew F.
Maegan L. 3
Toast
J.J. H.
Jordan P.
Angel A.
Emma L. 4
Josh J.
Rachel M.
Ty K.

5. Section 2
Graphs and Statistics

6. Quantitative Data Set Measure of Center 5 Number Summary:
Mean: 2.1
Minimum: 0
Median: 2
Q1: 1
Mode: 2
Median (again): 2
Mean Absolute Deviation (MAD): 1.64
Q3: 3
Standard Deviation (SD): 2.21
Maximum: 8
Ranges
Range: 8
IQR: 2

7. Steps for Math
Mean: For this I added all of my data numbers together and got 69 as the sum and then divided by 30 to get 2.3 for my average or mean. IQR: 3-1= 2 (2 is Interquartile Range) Range: 8-0= 8 (Maximum-Minimum= Range)

8. MAD Mathematics: The Mean Absolute Deviation (MAD) is 1.64. Numbers
Absolute Value
Absolute
Value
2.3 2
0.3 1
1.3 3
0.7 4
1.7 5
2.7 6
3.7 7
4.7 8
5.7
MAD Mathematics:
The Mean Absolute Deviation (MAD) is 1.64.

9. SD Mathematics: The Standard Deviation (SD) is 2.21. Numbers Mean
Difference
Squared
2.3
-2.3
5.29 2
-0.3
0.09 1
-1.3
1.69 3
0.7
0.49 4
1.7
2.89 5
2.7
7.29 6
3.7
13.69 7
4.7
22.09 8
5.7
32.49
SD Mathematics:
The Standard Deviation (SD) is 2.21.

10. Quantitative Data Histogram

11. Description of Quantitative Data Graph
S.O.C.S.
Shape: The shape of this histogram is Skewed Right. This means that there are less data points on the right than there is on the left. It is also Unimodal because there is only one peak.
Outliers: The two outliers are 7, 7 and 8. This can be acquired by doing this formula: Q (IQR) and I did 3+1.5(2)=6. So anything above 6 is an outlier. I also did the formula Q (IQR) to determine if there were any outliers below the answer of the formula, but there were no outliers with that formula.
Center: Median because there are outliers and they don’t effect the median, only the mean.
Spread: The spread of this graph is IQR since the center is the median.

12. Best Measure of Center and Spread
Center: The center is the median because the graph is skewed and there are outliers making it better for the center to be the median. On the other hand, if it was the mean (it is not), there would have to be no outliers, a symmetrical graph and be close to the median, but since the graph does not meet any of that criteria, the best measure of center is the median. Spread: The best measure of spread is the Interquartile Range or the IQR because the center is the median. The IQR best measures the spread because it is able to describe the data better and more accurate while any other spread, would result in an inaccurate display of the data.

13. Categorical Data Circle Graph
Note:
Some of the ways I rounded make the totals seem off, but it is actually correct.
Toast
Apples
Oranges
Carrots
Cookie
Cereal
Nothing
Total 2 4 3 1 14 30
6.7%
13.3%
10% 3%
47%
100%

14. Biases
As hard as I tried to have no bias, biases still appeared in the survey.
Avoided Biases
I started out by having a clean, neat questions got the same number of boys and girls and as random of people as I could muster. I tried to avoid biases by having everyone hear the same question in the same order and tried to make it as least pressuring on them as possible so they didn’t feel like they had to answer one way or another.
The second one is that I didn’t always have them take the survey the same way. But I always tried to give them the paper so they could fill it out without feeling pressured, When I had them fill out the sheet where other people had answered, they on my Quantitative question, they might have been inclined to answer a bigger number of the times they traveled out of state to seem more impressive.
Some Biases
Some people also might not have had accurate information. For example what kind of snack they felt like at that moment, not a general answer or might not have remembered how many times they went out of state this summer.
The first one is that sometimes what I asked and said was a little bit different. Sometimes I would start out my survey like this: “Do you want to take my survey?” or “Do you want to take a survey?” Not a terribly big difference, but could create some bias.

15. Section 3
Quantitative Data Comparison

16. Box and whisker plot 5 Number Summary
Trips for People With Glasses/Contacts
Minimum:
Quarter 1: 1
Median: 2
Quarter 3: 3
Maximum: 8
Box and whisker plot
5 Number Summary
Trips for People Without Glasses/Contacts
Minimum:
Quarter 1: 1
Median: 2
Quarter 3: 3
Maximum: 5

17. Centers and Spreads Glasses/Contacts
No Glasses/Contacts
Center:
Mean: 2.45
Mean: 2
Median: 2
Mode: 2
Spreads:
Range: 8
Range: 5
Interquartile Range: 2

18. Comparisons
In the Box and Whisker Plot in Section 3, people with Glasses/Contacts took more trips (4 more trips but the boxplot doesn’t show that) than people without Glasses/Contacts. This shows that even though eyewear can cost a lot of money, it doesn’t effect the amount of trips they took. Also, the people with glasses/contacts took way more trips as individuals and that the extra cost didn’t effect the amount of vacations they took. My first observation is that eyewear either doesn’t effect the amount of vacations they take or it helps them have more vacations.
All the information for the spreads and the center are the same except for the mean. This shows that even if there aren’t any outliers, there is a number or more than one number that are outlier(s). It shows how one number (in this case a few) can change how the outcome is different. In Section 3, Centers and Spreads, it shows how little changes or differences can make a “ripple effect” which means that a little differences effects more and more information down the line. My second observation is that a little difference is what makes can make a larger difference later.

19. Section 4
Categorical Data Comparison

20. Side By Side bar graph x

21. Distributions Toast Apples Oranges Carrots Cookie Cereal Nothing Total
With Contacts/Glasses 1
0.035
3.5% 4
0.14
14% 2
0.07 7% 8
0.27
27% 20
0.69
69%
Without Contacts/Glasses
0.0 0% 6
0.2
20% 10
0.34
Totals 3
0.105
10.5% 14
0.47
47% 30
1.0
100%

22. Comparisons
According to the data for Section 4, side by side bar graph is splayed all over the place. The amount of data is everywhere, not one place hogs it. Except the cereal. The majority of both people with and without glasses/contacts both wanted cereal as their afterschool snack. Cereal was a definite outlier because all the information was mostly clogged up there and not anywhere else. My first observation is that all the information is splayed out except for the cereal which hogs most of the surveyors’ stomachs.
Cereal has almost 50% of the surveyors based on the Section 4, Relative Frequency Table. This shows a common interest in the population. Also, 2/3 of the people that were randomly surveyed had glasses/contacts and only 1/3 of the people didn’t have glasses/contacts. This shows how much more people have glasses than not. My second observation is that more people liked cereal than people had glasses/contacts. Your eyewear does not effect your taste in food.

23. Section 5
Final Analysis

24. Final analysis
In what ways does your survey support/answer your question?
I wanted to know whether people wore glasses/contacts or not, how many times people traveled out of state, and what snack they preferred afterschool. This survey helped me quite a bit because it showed me that about 2/3 of the people I surveyed had eyewear. People generally, most commonly, traveled out of state two times and this could help me plan for the future. And people prefer cereal for afterschool snack if I ever wanted to plan or help with a future event.
What did your survey not adequately address? What data would you need to collect to better answer your question?
I would want to address that there were a lot of different snacks that people would want. I would have wanted a couple more options for snacks afterschool. I limited the people’s choices, so I couldn’t get a better representation of what people actually liked for a snack.
3. What next steps would you recommend?
I would recommend taking he same survey, but survey a lot more people and a more variety of people. Not limiting it to 8th Grade GT. I would get a better representation of the population and try to eliminate some of the biases.

25. Thanks for watching!
By Ella Hill 1*