1. Construct a bar graph for a frequency distribution and for a relative frequency distribution for a qualitative variable. 2. Construct a pie chart for the qualitative variable. Quantitative data 1. Construct a histogram for your survey’s numerical data. Make sure that your histogram has an appropriate width for the classes. Explain why your choice for the width makes sense for your specific data. 2. Create a boxplot for the variable. 3. Write a desсrіption of each graph (What does each graph show you about your data, that you won’t be able to easily see in the other graphs?). 4. Find the following sample statistics for the data set: Minimum value, Maximum value, Mean, Median, Mode, Q1, Q3, Range, IQR, and Standard Deviation. For each of these values write a sentence explaining what it tells you about the results in your survey. Please do not write about how they are calculated. The purpose of this exercise is to make sure that you understand the meaning for each of these statistics (not how you find it). So please don’t include steps for finding each of these. You will be graded on your explanation of what each value tells us specifically about your sample. 5. Describe and analyze the numerical data. What is the overall shape of the data set? Based on your answer, determine which measure of center (mean, median or mode) you think is best and why. Determine which measure of spread (IQR / standard deviation or range) you think is best and why. Write a sentence explaining the real meaning of the center you found and a sentence explaining the real meaning of the spread you have found for your data. 6. Create a written report including all your findings from the questions above. What did you learn about the population of your interest from your data analysis. You should have an introduction paragraph discussing why this topic was important in the world or important to you and a conclusion paragraph summarizing your findings. Your report should be at least one page, double spaced (font 12) not counting graphs. The Empirical Rule and Normal Distribution 1. Discuss properties of a normal curve 2. Use the normal model and the empirical rule to find estimates for the proportion of data that falls within 1 standard deviation of the mean. 3. Use the normal model and the empirical rule to find estimates for the proportion of data that falls within 2 standard deviations of the mean. 4. Use the normal model and the empirical rule to find estimates for the proportion of data that falls within 3 standard deviations of the mean. 5. Use a real-life example where data follows normal distribution. Apply empirical rule to answer the following questions: a. What two values will have approximately 95% of the data between them? b. Describe where will the top (highest) 2.5% of the data will lie on the distribution? c. Describe where will the bottom (lowest) 2.5% of the data will lie on the distribution? d. What two values will have approximately 68% of the data between them? e. What two values will have approximately 99.7% of the data between them?
