AP Statistics Exploring Normality Name ______
I. How Can We Assess Normality?
a. List three characteristics of all normally distributed data.
b. Is any data perfectly normal? Explain.
c. Given a set of data and your answer to questions a&b above, list at least 2 methods that you already know that you could use to determine if the data is normal.
d. Do you think that a large set of data is more likely to be normal than a small set of data? For example, if we examined the heights of students in our class (a small set of data) and compared it to the heights of high school students in the United States, would we get a different distribution?
II. Assessing Normality
a. United States 2009 Unemployment Rates: the following chart shows the unemployment rates in all 50 states from November, 2009. The data is arranged from lowest (North Dakota) to highest (Michigan)
4.1 / 4.5 / 5.0 / 6.3 / 6.3 / 6.4 / 6.4 / 6.6 / 6.7 / 6.7 / 6.7 / 6.9 / 7.07.0 / 7.2 / 7.4 / 7.4 / 7.4 / 7.8 / 8.0 / 8.0 / 8.2 / 8.2 / 8.4 / 8.5 / 8.5
8.6 / 8.7 / 8.8 / 8.9 / 9.1 / 9.2 / 9.5 / 9.6 / 9.6 / 9.7 / 10.2 / 10.3 / 10.5
10.6 / 10.6 / 10.8 / 10.9 / 11.1 / 11.5 / 12.3 / 12.3 / 12.3 / 12.7 / 14.7
Plot the data. Use a dotplot, stemplot or histogram. Describe the Distribution.
b. Does the data follow the empirical rule? Complete the table to find out and alayze your results against what you would expect from the Empirical Rule.
Mean = ______Standard Deviation = ______
Low Vale / High Value / Frequency / Percent of Dataμ∓1σ
μ∓2σ
μ∓3σ
c. Create a box plot of the data. Describe the distribution.
d. Does the data appear approximately normal? Why or why not? Be sure to CUSS.
A Normal Probability Plot shows each observation (x) plotted against its expected z-score (y). Perfectly normal data is linear. Remember, however that virtually no data is perfectly normal, so we should not overreact to slight variations from normal when we assess normaility. Look for a linear pattern, but don’t overreact to minor wiggles in the plot. Look for shapes that show clear departures from Normality.
III. Using your calculator, construct a Normal Probabiliity Plot for the Unemployment Rate data. Describe the data. Is it approximately normal? Why or why not?
IV. Guinea Pig Survival times: Scientists conducted an experiment using Guinea Pigs and tracked their survival times (in days) after they were injected with an infectious bacteria.
43 / 45 / 53 / 56 / 56 / 57 / 58 / 66 / 67 / 73 / 74 / 7980 / 80 / 81 / 81 / 81 / 82 / 83 / 83 / 84 / 88 / 89 / 91
91 / 92 / 92 / 97 / 99 / 99 / 100 / 100 / 101 / 102 / 102 / 102
103 / 104 / 107 / 108 / 109 / 113 / 114 / 118 / 121 / 123 / 126 / 128
137 / 138 / 139 / 144 / 145 / 147 / 156 / 162 / 174 / 178 / 179 / 184
191 / 198 / 211 / 214 / 243 / 249 / 329 / 380 / 403 / 511 / 522 / 598
a. In your calculator, construct a histogram of the data. Describe the distribution.
b. Using your calculator, construct a Normal Probability Plot of the data. Describe the plot.
c. Is the data approximately normal? Why or why not?
V. Below is a stem and leaf plot showing NBA Free-Throw Percents.
a) Describe the distribution.
b) What would you expect the Normal Probability Plot to look like? Sketch it her.