MAT 152 Signature Assignment The purposes of the project are to distinguish between quantitative and qualitative data, to demonstrate both an understanding of the appropriate means of displaying, analyzing and interpreting statistics on each type, and the appropriate use of technology to produce a report of the findings. Project Outline 1. Pick a meaningful survey topic that can be investigated by asking people in your surroundings (students, coworkers, neighbors, etc.). Identify and explain how the sample was selected. You must survey at least 30 people. 2. Your survey must contain 3 questions: a. 1 question that has a qualitative (word) response b. 2 questions that give a quantitative (numeric) response that you think may have a relationship. 3. You must get your instructor to approve the survey. 4. Collect and compile the data. The report you submit must include the following: 5. An introduction, explaining what topic is being investigated and how the survey was conducted. Identify and explain how the sample was selected. Is it biased?? If so, why? How could you have taken a better survey? 6. Using SPSS, A. For the qualitative data 1. Create a frequency table 2. Create a pie chart and a Pareto chart 3. Find the mode. B. For the quantitative data. Pick one of your quantitative data questions and create the following tables/graphs. 1. Calculate the mean, median, mode, range, standard deviation, and five number summary. 2. Create a dot plot. 3. Create a box plot. 4. Identify any outliers. 5. Create a histogram using between 5 and 10 classes (Visual Binning). c. Using both of your quantitative questions, (using lab 6 as your guide), create/answer the following: 1. Determine which one you believe to be the explanatory variable and which is the response variable. 2. Construct a scatterplot 3. Graph the best fit line on the scatterplot 4. Find the correlation coefficient 5. Determine the regression equation of the best fit line (#7 is what is to be graded by the Critical Core Rubric) 7. Write an overall conclusion. This should include but is not limited to the following points: a. Look back at your qualitative data, state the mode and any trend in your data. b. Look back at #6b, discuss the findings. What is your mean and median? Based on this information is your graph skewed? Do you have any outliers and were you surprised by the outliers? What did you find interesting about your findings. c. Look back at #6c, i) What did you believe the explanatory and response variables were? ii) Did your scatterplot show a linear correlation? What was the linear correlation? Is this what you expected? iii) What is your least squares regression line? What does the slope and y-intercept mean in the case? Are you able to interpret the y-intercept? Why or why not?
iv)what did you find interesting from the results of your two quantitative questions? v) If you were to do this project over again, would you do anything differently? MAT 152 SPSS Project Grading Rubric Points Possible Your Points Introduction 5 SPSS used to Generate Graphs 3 Qualitative Data Frequency Table 3 Qualitative Data Pie Chart 3 Qualitative Data Pareto Chart 3 Qualitative Data Mode 3 Quantitative Data Mean 3 Quantitative Data Median 3 Quantitative Data Mode 3 Quantitative Data Range 3 Quantitative Data Standard Dev. 3 Quantitative Data 5-Num. Summary 3 Quantitative Dot Plot 3 Quantitative Box Plot 3 Quantitative Outliers Identified? 3 Quantitative Histogram 3 Quantitative Explanatory/Response 3 Quantitative Scatterplot 3 Quantitative Fit line on Graph 3 Quantitative Correlation Coeff. 3 Regression Line 3 Organization/Neatness of Project 20
Conclusion 15 Total Points Possible 100 Late? -10% (per day late) x days Days late begin at 11:59 p.m. New Total Score if Late Comments: CRITICAL CORE Central Piedmont Community College has identified Communication, Critical Thinking, Personal Growth & Cultural Literacy, and Information Technology & Quantitative Literacy as 21 st century skills expected by both employers and four-year educational institutions. All graduates are required to complete course work that demonstrates acquisition of these critical core competencies, which are crucial to personal, academic, and professional success. These competencies are demonstrated throughout the content of the course, discipline or program of study, and complement basic program knowledge and application. MAT 152 is aligned Information Technology and Quantitative Literacy and will focus on providing students the opportunity to attain and document the following ability: APPLY QUANTITATIVE CONCEPTS TO INTERPRET DATA The following rubric illustrates your expected path of growth in the competency: Beginning Emerging 1 Attempts to explain information presented in mathematical forms, but draws incorrect conclusions about what the information means. For example, attempts to explain the trend data shown in a graph, but will frequently misinterpret the nature of that trend, perhaps by confusing positive and negative trends. 3 2 Provides somewhat accurate explanations of information presented in mathematical forms, but occasionally makes minor errors related to computations or units. For instance, accurately explains trend data shown in a graph, but may Provides accurate explanations of information presented in mathematical forms. For instance, accurately explains the trend data shown in a graph. Proficient 4 Provides accurate explanations of information presented in mathematical forms. Makes appropriate inferences based on that information. For example, accurately explains the trend data shown in a graph and makes reasonable predictions regarding what the data suggest about future events
miscalculate the slope of the trend line How does the grading rubric and the Critical Core Rubric relate? A large part of the assignment is the conclusion. The students are expected to go back through their data and graphs and explain trends or describe their findings. Therefore in the grading rubric, the conclusion is worth 15 % of their final assignment grade. For the Critical Core Rubric, the instructor is to only look at the conclusion and the directions from the signature assignment for part #7. You are not grading on whether the tables and graphs are accurate. The instructor is looking to see if the student answered all the questions asked in #7 and then use the crucial core rubric to determine if the conclusion is at a competency level of 1, 2, 3, or 4. This score does not correspond directly to the student s signature assignment grade. (However, there is probably a strong correlation.) Below are examples of each rubric score and an explanation to why the rubric score was given. Example of a Rubric score of 4 This student received a 4 as the Critical Core Rubric Score. This student successfully included answers to all the questions from #7 in the conclusion. The student accurately explained what the mean and median were and what this means for the graph and explains the outliers. Also explains why the outliers were expected. Also clearly identifies and explains the explanatory/response variables and the correlation between the variables. The student stated the least squares regression line and explained what the y-intercept and slope mean for the data he/she has found. Lastly, it is clearly the student thought about what would make this a better survey and what was learned from this experience. INTRODUCTION The topic I chose focused on college students. The qualitative question was What is your college major? The two quantitative questions were How many credit hours are you taking this semester? and How many hours do you spend doing hw or studying each week? To gather the sample of students I sent a text to my friends asking if they can respond to my survey. Although I was successful in collecting my responses, there was bias in my results because I constructed the survey based on convenience, and it limited responses to a small population. However, all of the people I asked were the same age so there was consistency in other factors that may have played a role in their responses. My goal for this project was to see if there was a relationship between how many credit hours of classes students take in a semester, and how many hours a week they spend studying/doing H.W for their classes. Also, I wanted to see if what they are majoring in plays a role. Frequencies Statistics College Major N Valid 30 Missing 0
College Major Frequency Valid Cumulative Valid Business 6 20.0 20.0 20.0 Doctor 2 6.7 6.7 26.7 Education 5 16.7 16.7 43.3 Engineer 1 3.3 3.3 46.7 Nurse 9 30.0 30.0 76.7 Psychology 3 10.0 10.0 86.7 Physical 2 6.7 6.7 93.3 Therapist Speech Pathology 2 6.7 6.7 100.0 Total 30 100.0 100.0
Mode for the qualitative data: Nurse Statistics Credit Hours N Valid 30 Missing 0 Mean 15.47 Median 15.00 Mode 15 Std. Deviation 1.167 Range 5 Minimum 13 Maximum 18 iles 25 15.00 Dot Plot 50 15.00 75 16.00
Statistics Credit Hours N Valid 30 Missing 0 Mean 15.47 Median 15.00 Mode 15 Std. Deviation 1.167 Range 5 Minimum 13 Maximum 18 iles 25 15.00 50 15.00 75 16.00
Dependent Variable: Hours Studying Independent Variable: Credit Hours taken this semester Credit Hours Hours Studying Correlations Hours Credit Hours Studying Pearson 1.881 ** Correlation Sig. (2-tailed).000 N 30 30 Pearson Correlation.881 ** 1
Sig. (2-tailed).000 N 30 30 **. Correlation is significant at the 0.01 level (2-tailed). Regression Model Variables Entered/Removed a Variables Variables Entered Removed Method 1 Credit Hours b. Enter a. Dependent Variable: Hours Studying b. All requested variables entered. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1.881 a.776.768 1.737 a. Predictors: (Constant), Credit Hours ANOVA a Model Sum of Squares df Mean Square F Sig. 1 Regression 292.992 1 292.992 97.115.000 b Residual 84.475 28 3.017 Total 377.467 29 a. Dependent Variable: Hours Studying b. Predictors: (Constant), Credit Hours Coefficients a Unstandardized Coefficients Standardized Coefficients Model B Std. Error Beta t Sig. 1 (Constant) -32.608 4.288-7.604.000 Credit Hours 2.725.276.881 9.855.000 a. Dependent Variable: Hours Studying
CONCLUSION Overall, the results obtained by this survey were what I expected. For the qualitative data, the mode was majoring as a nurse. It is common that people want to work in the medical field so it only makes sense that this was a common response. Other top responses included education, and business, which are two jobs that have high demand. For the quantitative data, I chose to analyze the credit hours students take in a semester. This seemed to range from 13-18 in a semester, which demonstrates that everyone that was surveyed are full time students. The mean (15.47) and median (15) were similar which can be seen by the approximately symmetrical graphs. Although the distribution had a symmetrical distribution, it appeared that there were outliers. These outliers can be shown on the box plot, with one at 13 and two at 18 credit hours. It makes sense that these are outliers because 13 credit hours is just enough to be considered a full time student, and 18 is the max you can take. When comparing the two quantitative results, I identified the credit hours as the explanatory variable (independent) and the hours spent studying as the response variable (dependent). The scatterplot demonstrated a linear relationship which makes sense since the correlation coefficient,.776, is close to 1. The least squares regression line is represented by the equation y=2.72x-32.61. The y-intercept can t be interpreted because you can t study a negative amount of hours. The slope can be interpreted as for every additional credit hour taken, a student will study approximately 2.72 hours more. I found it interesting that although for the most part the more credit hours a student takes, the more hours they spend studying, there were a few cases where this wasn t true. I believe this is due to certain lurking variables that influence the result such as having a job, volunteer work, extracurricular activities or sports, and other aspects of someone s everyday life. As stated in the intro, since the way I conducted my survey had bias, if I were to do this project again I would use a different method. It would be best to make sure all the students go to the same school since you could be certain they have the same opportunities. If just looking for the quantitative results, it would beneficial to ask students who have the same major. Also, asking a larger sample, and not doing it based on convenience would help strengthen the positive relationship that was seen between the number of credit hours a student takes in a semester, and how many hours a week they spend studying. Example of a Rubric Score of 3 This student received a 3 as the Critical core Rubric score. The student answered all the the part of #7 in the conclusion. Therefore a score of 3 provides accurate explanations of information. However, the student answered all the parts but did not add any extra details. The student stated what the y- intercept and slope was but did not explain the meaning of these answers. Also the last two questions are very basic without much additional inferences or extra explanations of the data. Introduction: The topic I investigated was if there was any correlation between the numbers of hours people worked versus their GPA. The sample I collected was just asking friends on my phone and also asking other CPCC students. I don t think my survey is too biased because I asked random CPCC students as well as my
friends from different schools. I could have taken a better survey if maybe I asked more people to get more accurate results. Favorite Color Frequency Valid Cumulative Valid Blue 12 40.0 40.0 40.0 Green 3 10.0 10.0 50.0 Pink 7 23.3 23.3 73.3 Purple 4 13.3 13.3 86.7 Red 4 13.3 13.3 100.0 Total 30 100.0 100.0
Statistics hours worked N Valid 30 Missing 0 Mean 20.93 Median 18.00 Mode 0 a Std. Deviation 13.078 Range 60
Minimum 0 Maximum 60 iles 25 13.50 50 18.00 75 27.50 a. Multiple modes exist. The smallest value is shown
hours worked Statistics N Valid 30 Missin g 0 Mean 20.93
Median 18.00 Mode 0 a Std. Deviation 13.078 Range 60 Minimum 0 Maximum 60 ile s 25 13.50 50 18.00 75 27.50 a. Multiple modes exist. The smallest value is shown
Correlations hours worked GPA hours worked Pearson Correlation 1 -.475 ** Sig. (2-tailed).008 N 30 30 GPA Pearson Correlation -.475 ** 1 Sig. (2-tailed).008 N 30 30 **. Correlation is significant at the 0.01 level (2-tailed). Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1.475 a.225.198.35766 a. Predictors: (Constant), hours worked Coefficients a Unstandardized Coefficients Standardized Coefficients Model B Std. Error Beta t Sig. 1 (Constant) 3.223.125 25.835.000 hours worked -.014.005 -.475-2.853.008
a. Dependent Variable: GPA Conclusion: a.) Looking back at my qualitative data I saw that blue was the mode because it was the most frequently picked. b.) After looking back at 6b I found my mean was 20.93 and median was 18 and my graphed was skewed. I had an outlier and was surprised because 60 is a lot of hours to work for a college student. Besides the outliers I was not too surprised by the data because I feel most of the data correlates. c.) The explanatory would be hours worked and response would be GPA ii.) My data only correlated with a few values but for the most part there was no correlation. I was not expecting that because for the most part I thought there was a relation. iii.) The least squares regression line in y=3.22-.001x and y-intercept is 3.22 and slope is.001x. iv.) I thought what was most interesting from my quantitative data was some of the hours these people work and still manage to have decent grades. v.) If I were to do this project differently I might have asked a few more people to better my results. Example of a Rubric Score of 2 This student received a 2 as the Critical Core Rubric score. The student some of the questions from #7 parts a and b. The student also tries to answer parts of c for instance explaining the outliers and the linear correlation. However there is no line to go with the data and therefore no interpretation of this information. Therefore this would be a somewhat accurate explanation of the information presented. SPSS Signature Assignment SPSS is a popular statistic system that students use to generate graphs and find all statistical functions through. Throughout the course of the semester students were asked to complete lab assignments to generate an understanding on how the system works. This signature assignment brings all the skills we learned throughout the year into one huge lab. When viewing all the data results I can understand all the work I have done. My
Qualitative data question was What Color is Your Car? I surveyed 30 students who go to CPCC, from this survey my results was that the mode color was black and other. The trend was wavy, it varied. I asked students about how many cars they own and what year their cars were made. My data for 6b mode was the year 2011, mean was 2010. My data did not conclude into having an outlier. Many people only owned one car so when I put in my data I have everyone at owning one car and many people own a 2011 car. When viewing 6c data the data shows that everyone owns only one car so most of the separation is by year. My data collected shows that many people own cars from various years. My scatter plot, let s say did not scatter. Since my x-value was cars owned my liner correlation line is there, extremely noticeable. My two quantitative questions caused my data to show results exactly. This resulted in no outliers. Since my x-value was cars owned my liner correlation line is there, extremely noticeable. My two quantitative questions caused my data to show results exactly. This resulted in no outliers. In conclusion, my data helped me improve my skills in SPSS. I enjoyed talking to people about their cars. I should have chosen a more explanatory question to collect more conclusive data about cars owned. My project if done over again would have had a different quantitative question. The work done throughout this assignment has made me learn that SPSS is an extremely helpful tool for creating accurate statistical graphs. Color of Cars Frequency Valid Cumulative Valid Black 9 30.0 30.0 30.0 Blue 7 23.3 23.3 53.3 Other 9 30.0 30.0 83.3 White 5 16.7 16.7 100.0 Total 30 100.0 100.0
Year Made Statistics N Valid 30
Missing 0 Mean 2010.50 Median 2011.00 Mode 2011 Std. Deviation 4.607 Range 16 Sum 60315 Year Made Frequen cy Percen t Valid Cumulativ e Vali d 200 1 200 3 200 4 200 5 200 8 200 9 201 0 201 1 201 2 1 3.3 3.3 3.3 1 3.3 3.3 6.7 2 6.7 6.7 13.3 3 10.0 10.0 23.3 2 6.7 6.7 30.0 3 10.0 10.0 40.0 1 3.3 3.3 43.3 4 13.3 13.3 56.7 3 10.0 10.0 66.7
201 3 201 4 201 5 201 6 201 7 Tota l 1 3.3 3.3 70.0 1 3.3 3.3 73.3 3 10.0 10.0 83.3 2 6.7 6.7 90.0 3 10.0 10.0 100.0 30 100.0 100.0 Descriptive Statistic Std. Error Year Made Mean 2010.50.841 95% Confidence Interval for Mean Lower Bound 2008.78
Upper Bound 2012.22 5% Trimmed Mean 2010.63 Median 2011.00 Variance 21.224 Std. Deviation 4.607 Minimum 2001 Maximum 2017 Range 16 Interquartile Range 8 Skewness -.329.427 Kurtosis -.857.833 Statistics
Year Made N Valid 30 Missing 0 Mean 2010.50 Median 2011.00 Mode 2011 Std. Deviation 4.607 Range 16 Sum 60315 Explanatory - Year Cars are Made Response- Number of Cars
Example of a Rubric 1 This student received a 1 as a Critical Core Rubric Score. The conclusion is hard to follow. There are some findings and data reported. It does talk about whether or not the data is skewed and does make an attempt at what he/she would change in the future. However, the data and information are greatly lacking in this conclusion. (If you look back at the graphs and tables there are several of the required parts missing. Again we are not actually looking at the graphs for the rubric, only what is written in the conclusion.) SPSS Statistic Assignment Introduction On April 20th, my class was issued a project to utilize quantitative and qualitative data and recognize them within a chart to be issued to others that see it. The tools I needed to attempt this project was my handydandy TI-84 calculator, pen and paper and the Statistical Package for the Social Sciences or just SPSS for short. The SPSS is a software package used in statistical analysis of data. My first step was to find quantitative and qualitative data and have thirty people respond to what they had, I decided to keep it simple by asking students what color their houses were and how many windows that they had; however I had a minor problem with that. In the assignment the qualitative data had to be affected by two quantitative data pieces, which I If done my house idea it won t have changed so I had to alter my assignment. I changed it to asking students that attended CPCC if they were full time or part time for qualitative data and asking how many classes they had and how many credit hours they had. My results were that 23 student registered as full time with the average amount of hours being 16 and 6 classes. Frequency Table Full Or Part Frequency Valid Cumulative Valid Full 22 73.3 73.3 73.3 Part 8 26.7 26.7 100.0
Total 30 100.0 100.0 Bar Chart statistics FullOrPart Hours N Valid 30 30
Missing 0 0 Frequency Table Frequency FullOrPart Valid Cumulative Valid Full 22 73.3 73.3 73.3 Part 8 26.7 26.7 100.0 Total 30 100.0 100.0 Frequency Hours Valid Cumulative Valid 12.00 7 23.3 23.3 23.3 16.00 13 43.3 43.3 66.7 17.00 8 26.7 26.7 93.3 18.00 2 6.7 6.7 100.0 Total 30 100.0 100.0 Bar Chart
FullOrPart Frequency Valid Cumulative Valid Full 22 73.3 73.3 73.3 Part 8 26.7 26.7 100.0 Total 30 100.0 100.0 Frequency Classes Valid Cumulative Valid 3.00 5 16.7 16.7 16.7 4.00 3 10.0 10.0 26.7 5.00 5 16.7 16.7 43.3 6.00 12 40.0 40.0 83.3 7.00 5 16.7 16.7 100.0 Total 30 100.0 100.0 Pie Chart
Frequency Table Frequency FullOrPart Valid Cumulative Valid Full 22 73.3 73.3 73.3 Part 8 26.7 26.7 100.0 Total 30 100.0 100.0
Hours Frequency Valid Cumulative Valid 12.00 7 23.3 23.3 23.3 16.00 13 43.3 43.3 66.7 17.00 8 26.7 26.7 93.3 18.00 2 6.7 6.7 100.0 Total 30 100.0 100.0
Conclusion My conclusion is that 73.3 percent of students reported that they were full time leaving 26.7 percent of students we part time. Majority of students had a total of 6 classes. The least amount of classes were 4 classes. The best thing about this is that weeks from now we can go back to these charts here and go over the information that been already accessed. So we can revaluate any corrections that we need. Looking back on the survey there was no outliers. The information wasn t screwed in any way. However I probably should stick to one campus instead of getting answers from students that went to other campuses because some of my participants were in middle college. I didn t find anything too interesting from the results of my two quantitative questions I had already hypothesized that majority of the students were full time as well.