Weaymouth,+S

__//Stage 1//__: Initial Proposal


 * Brainstorming:**

1. Number of work hours a week vs. Highschool Average 2. Teen pregnancy rates vs. Highschool Graduates 3. Student Involvement within the school vs. Highschool Average 4. Students who don't eat breakfast vs. Average 5. Students involved in Extra Curricular activities vs. Averages

Dependent Variable: **Extra Curricular Activities** Independent Variable: **Students Average**

= __VS__. =

Is there a strong correlation between Extra Curricular Activities and Grade Averages? Does extra curricular activities affect the students of Ancaster High School's averages throughout the various grades?
 * Question:**

I believe there will be a positive moderate correlation coefficient once the data is graphed because i feel when i myself am involved with extra curricular activities it can be challenging to keep up with my schooling. Also, i have heard many students say they couldn't hand in an assignment on the day it's due or write a test on the test day, due to an extra curricular activity that they are involved in.
 * Hypothesis:**

This Survey is //__ANONYMOUS.__// __http://www.zoomerang.com/Survey/WEB22BGPVMJPXC/__
 * The link below is the survey i will ask students in all grades at Ancaster High to complete:**




 * Hard Copy of Survey:**

1) What Grade are you currently in? [ ] 9 [ ] 10 [ ] 11 [ ] 12 [ ] Post Graduate

2) In one school year, How many Extra Curricular Activities do you evolve yourself in? [ ] 0  [ ] 1  [ ] 2  [ ] 3  [ ] 4  [ ] 5+

3) If you answered 1 or above in the previous question, please list the Activities below...

4) Please enter your current average

5) Please rate yourself on how you feel you keep up with your schooling while taking part in extra curricular activities

Keeping up with homework: [ ] Poor [ ] Fair [ ] Good [ ] Excellent

Keeping up with assignments: [ ] Poor [ ] Fair [ ] Good [ ] Excellent

6) On average, Do you feel you miss a lot of school because of an activity? [ ] Yes  [ ] No  [ ] Other, please specify:

7) How many hours per week do you involved yourself in extra curricular activities? [ ] 0 [ ] 1 [ ] 2 [ ] 3 [ ] 4 [ ] 5 [ ] 6 [ ] 7 [ ] 8 [ ] 9 [ ] 10 [ ] 11 [ ] 12+

Raw Data This survey is one of my Sampling Techniques that i will be using to collect my data. A population may include groups of members who share common characteristics such as age or gender. - These groups are known as a strata - A stratified sample has the same proportion of members from each stratum of the population
 * 1) Stratified Sample Technique:**

In order to collect my data, i have made a simple survey that i will ask the same amount of people from each grade: 9-12 at Ancaster High School to complete. In order to get an accurate set of data I will ask the different grades these simple questions from the survey, because the people in the grades share common characteristics such as age, gender, and race. Having asked many different people throughout the school to complete this survey will leave me to have more accurate information instead of just asking one grade or just my friends.

Technique in which part is at the discretion on initiative of the respondent. - Voluntary response samples are things like mailed-out surveys, The participants are able to choose whether they would like to participate or not. - This causes some forms of Bias, because only the participants usually have strong opinions on the subject. People who could care less about the issue are less likely to respond
 * 2) Voluntary Response Sample:**

When handing out my surveys to be answered, i will be giving the person a chance to choose in whether or not they would like to be surveyed on the topic. If by some reason they don't then i won't survey them. All surveys will be written anonymous, there is no need to have a name on the completed surveys.

**Survey Results**
__**Answers to the questions:**__


 * 1) **What grade are you currently in?**
 * 9** [35 answered]
 * 10** [46 answered]
 * 11** [50 answered]
 * 12** [50 answered]
 * Post Grad** [12 answered]
 * __Total:__ 193 people took the survey**


 * 2. In one school year, how many extra curricular activities to you evolve yourself in?**
 * 0** [46 answered]
 * 1** [74 answered]
 * 2** [28 answered]
 * 3** [40 answered]
 * 4** [3 answered]
 * 5+** [2 answered]

Student Council [32 answered] Soccer [12 answered] Band [7 answered] Singing [1 answered] Volunteering [10 answered] Student Newspaper [1 answered] Dance class [4 answered] Cross Country [2 answered] Water polo [4 answered] Volleyball [17 answered] Rugby [3 answered] Softball [2 answered] Badmiton [11 answered] Baseball [15 answered] Basketball [26 answered] Field Hockey [6 answered] Invisible Children [1 answered] Eco-Ninjas [2 answered] Deca [3 answered] Touch Football [5 answered] Art Club [4 answered] Intramurals [3 answered]
 * 3. If you answered 1 or above in the previous question, please list the Activities below... **
 * Total # of activities people are evolved in per year: 171**

61% [1 answered] 65% [2 answered] 66% [1 answered] 69% [2 answered] 70% [4 answered] 71% [1 answered] 72% [1 answered] 75% [14 answered] 77% [28 answered] 80% [41 answered] 81% [6 answered]] 82% [19 answered] 83% [11 answered] 84% [6 answered] 85% [32 answered] 86% [14 answered] 88% [4 answered] 90% [2 answered] 91% [2 answered] 92% [1 answered] 96% [1 answered]
 * 4. Please enter your current average **


 * 5. Please rate yourself on how you feel you keep up with your schooling while taking part in extra curricular activities **

Bottom % is percent of the total respondents selecting the option. || Poor || Fair || Good || Excellent || 31% || 37 19% || 56 29% || 40 21% || 30% || 62 32% || 39 30% || 34 18% ||
 * < Top number is the count of respondents selecting the option.
 * < Keeping up with Homework || 60
 * < Keeping up with Assignments || 58


 * 6. On average, Do you feel you miss a lot of school because of an activity? **
 * Yes** [ 64 answered]
 * No** [106 answered]
 * Other** [23 answered] **examples given were: skipping, sick, appointments, depending on certain times in the year, take a trip.**

[4] 0 [0] 1  [2] 2  [6] 3  [10] 4  [8] 5  [6] 6  [2] 7  [14] 8  [17] 9  [33] 10  [50] 11  [53] 12+
 * 7. How many hours per week do you involved yourself in extra curricular activities?**


 * After calculating all the data up that was received from the survey, i noticed that many of the students from Ancaster High could have been lying bout their answers to mess with my data or simply because they didn't know what answer to put down for some questions. Also, many of the students could have been lying about their averages because they didn't want me to see their average. Although i explained many times that this survey was anonymous.**
 * This is where i saw alot of:**

Response Bias

 * This occurs when participants deliberately give false or misleading answers. Respondents may want to influence results or they may be afraid or embarrassed to answer sensitive questions honestly.



//Are YOU Lying About Your Average?//

= **__Calculations__** =



To calculate it, add up the values of all the terms and then divide by the number of terms. //Mean Of Ancaster High School Student Averages // = 15,591/193 =80.78238342  = 81%
 * Mean:** the usual average



//Mean Of Hours a week Extra Curricular Activities occur //  = 1,933/193  =10.01554404  = 10 hours



**M edian:** the middle value Out of the 193 values, the median falls in between the 96th & 97th value. = (96+97)/2 =193/2 =96.5

**Mode:** the number that is repeated more often than any other Student Average= 80% Hours of Extra Curricular Activities per week= 12 hours

**Range:** the difference between the largest and smallest values  Student Average   = 96-61   = 35        Hours of Extra Curricular Activities per week = 12-1 = 11

**Standard Deviation:** a statistic that tells you how tightly all the various examples are clustered around the mean in a set of data xbar = 924.5/193 = 4.8
 * Interval || Frequency || Midpoint || Fimi || mi-u || (mi-u)2 || f(mi-u)2 ||
 * 0-1.5 || 4 || 0.75 || 3 || -4.05 || 16.4025 || 49.2075 ||
 * 1.5-3 || 2 || 2.25 || 5 || -2.55 || 6.5025 || 13.005 ||
 * 3-4.5 || 16 || 3.75 || 60 || -1.05 || 1.1025 || 17.64 ||
 * 4.5-6 || 8 || 5.25 || 42 || 0.45 || 0.2025 || 1.62 ||
 * 6-7.5 || 8 || 6.75 || 54 || 1.95 || 3.8025 || 30.42 ||
 * 7.5-9 || 14 || 8.25 || 115.5 || 3.45 || 11.9025 || 166.635 ||
 * 9-10.5 || 50 || 9.75 || 48.75 || 4.95 || 24.5025 || 1225.125 ||
 * 10.5-12 || 53 || 11.25 || 596.25 || 6.45 || 41.6025 || 2204.9325 ||
 * TOTAL || 193 ||  ||  Σ = 924.5 ||   ||   ||  Σ = 3708.6 ||

= √fi(mi-xbar)2/n-1 <span style="font-family: Arial,Helvetica,sans-serif;">= √3708.6^2/192 <span style="font-family: Arial,Helvetica,sans-serif;">=19.315625
 * <span style="font-family: Arial,Helvetica,sans-serif;">The Standard Deviation is 19.316


 * Correlation Coefficient**

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">r = __nΣxy – (Σx)(Σy)__ <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> √[nΣx₂ - (Σx)₂][nΣy₂ - (Σy)₂] <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">=__193(116196999) - (1810)(15489)__ <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px; line-height: 21px;">√[193(18650)-(1810)^2][193(1254223)-(15489)^2] = __2242601907 - 28035090__ <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px; line-height: 21px;">√(323350)(2155918) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px; line-height: 21px;">= __2214566817__ <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px; line-height: 21px;">√6.9712x10^11 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 14px; line-height: 21px;">= __2214566817__ 2.6403x10^11 =8.3875x10^19 r= 0.83875
 * The Correlation Coefficient is Positive Strong


 * Graph of My Data**
 * **Correlation**

<span style="font-family: Arial,Helvetica,sans-serif;">mean y= 15489 / 193 = 80.25 mean x = 1810 / 193 = 9.38 b=y-ax =80.25-(0.69268)(9.38) =73.75 y= 0.7x+73.75
In the beginning of this study, i predicted in my hypothesis that my information would create a Positive Moderate Correlation. After reviewing a lot of the surveys that the students throughtout grades 9-12+ completed, i noticed that many people who perform in many extra curricular activities a week had harder time juggling between their school work, test, and assignments. After i graphed my data and calculated my correlation coefficient the real results turned out to be a Strong Positive Coefficient. I also noticed that many of the students lied about their averages because they didn't want me to see it. The students may have just been guessing what their average is or they are just embarrassed about their mark. Although i said the survey was completely anonymous people still felt the need to not answer the average question truthfully. I felt alot of people didn't answer the whole survey truthfully because alot of the data that was presented was awkward.
 * Conclusion**