And Here We Go … Get ready to study for the AP Stats test!

1. And Here We Go … Get ready to study for the AP Stats test! Only 1050 minutes of class time until the big day… Friday,MAY 10!

2. How much studying will you do for $521.04? plus book…

3. The Exam ItselfTo maximize your score on the AP Statistics Exam, you first need to know how the exam is organized and how it will be scored. The AP Statistics Exam consists of two separate sections:

4. SCORING:Five open-ended problems @ 13 minutes; each counts 15 percent of free-response scoreOne investigative task @ 25 minutes; counts 25 percent of free-response scoreEach free-response question is scored on a 0 to 4 scale. General descriptors for each of the scores are: Your work is graded holistically, meaning that your entire response to a problem is considered before a score is assigned.

7. Calculator Policy • Each student is expected to bring to the exam a graphing calculator with statistical capabilities. The computational capabilities should include standard statistical univariate and bivariate summaries, through linear regression. The graphical capabilities should include common univariate and bivariate displays such as histograms, boxplots, and scatterplots. • You can bring two calculators to the exam. • The calculator memory will not be cleared but you may only use the memory to store programs, not notes. • For the exam, you're not allowed to access any information in your graphing calculators or elsewhere if it's not directly related to upgrading the statistical functionality of older graphing calculators to make them comparable to statistical features found on newer models. The only acceptable upgrades are those that improve the computational functionalities and/or graphical functionalities for data you key into the calculator while taking the examination. Unacceptable enhancements include, but aren't limited to, keying or scanning text or response templates into the calculator. • During the exam, you can't use minicomputers, pocket organizers, electronic writing pads, or calculators with QWERTY (i.e., typewriter) keyboards.

8. 2008-09 List of Graphing Calculators Graphing calculators having the expected built-in capabilities listed above are indicated with an asterisk (*). However, students may bring any calculator on the list to the exam; any model within each series is acceptable.

9. 1st AP Statistics test: 1997 ~ 7500 students 2008 AP Stat test: ~ 100,000 students

10. 1st AP Statistics test: 1997 ~ 7500 students 2009 AP Stat test: 116,876 students

11. 1st AP Statistics test: 1997 ~ 7500 students 2010 AP Stat test: ~ 109,609 students

12. 1st AP Statistics test: 1997 ~ 7500 students 2011 AP Stat test: ~ 137,498 students

13. 1st AP Statistics test: 1997 ~ 7500 students 2012 AP Stat test: ~ 143,554 students

14. The AP Statistics Exam covers material in these areas: • Exploring data: describing patterns and departures from patterns (20-30%) • Analyze data using graphical and numerical techniques • Emphasis on interpreting info from graphical and numerical displays and summaries • Sampling and experimentation: planning and conducting a study (10–15%) • Collecting data with a well developed plan • Clarifying the question and deciding on a method of data collection and analysis • Anticipating patterns: Exploring random phenomena using probability and simulations (20-30%) • Anticipating what the distribution of data should look like under a given model • Statistical inference: Estimating population parameters and testing hypotheses (30-40%) • Selecting appropriate models for statistical inferences

15. So. . . Let’s get started! What do you call data that has only ONE variable? UNIVARIATE DATA

16. What are the two types of univariate data sets? Categorical:qualitative (brand) Area codes Car you drive Type of computer you use Numerical: quantitative (numerical in nature) height Price of textbook Amount of cola in can

17. What are the two types of numerical data? Discrete: possible values are isolated points on a number line Number of AP classes Continuous: possible values form an interval (measurements are usually continuous) Distance lives from school

18. What are appropriate graphical displays for categorical data? • Bar Graphs • Bars do not touch • Categorical variable is typically on the horizontal axis • To describe – comment on which occurred the most often or least often • May make a double bar graph or segmented bar graph for bivariate categorical data sets

19. What are appropriate graphical displays for categorical data? • Pie Charts • To make: • Proportion X 360° • Using a protractor, mark off each part • To describe – comment on which occurred the most often or least often

20. What are appropriate graphical displays for numerical data? • Dot Plot • Used with numerical data (either discrete or continuous) • Made by putting dots (or X’s) on a number line • Can make comparative dotplots by using the same axis for multiple groups • Stem (and leaf) Plot • Used with univariate, numerical data • Must have key so that we know how to read numbers • Can split stems when you have long list of leaves • Can have a comparative stemplot with two groups (back to back)

21. What are appropriate graphical displays for numerical data? • Histograms • Used with numerical data • Bars touch on histograms • Two types • Discrete • Bars are centered over discrete values • Continuous • Bars cover a class (interval) of values • For comparative histograms – use two separate graphs with the same scale on the horizontal axis • Use no fewer than 5 classes (bars) • Check to see if scale is misleading • Look for symmetry and skewness

22. What are appropriate graphical displays for numerical data? Cumulative Relative Frequency Plot(Ogive) • . . . is used to answer questions about percentiles. • Percentiles are the percent of individuals that are at or below a certain value. • Quartiles are located every 25% of the data. The first quartile (Q1) is the 25th percentile, while the third quartile (Q3) is the 75th percentile. What is the special name for Q2? • Interquartile Range (IQR) is the range of the middle half (50%) of the data. • IQR = Q3 – Q1

23. What are appropriate graphical displays for numerical data? • Boxplot (and whisker) • Used with numerical data (either discrete or continuous) • Modified shows outliers • Can make comparative by showing side-by-side on same scale • Good for comparing quartile, medians, and spread

24. Why use boxplots? ease of construction convenient handling of outliers construction is not subjective (like histograms) Used with medium or large size data sets (n > 10) useful for comparative displays Why not use boxplots? • does not retain the individual observations • should not be used with small data sets (n < 10) • How to construct • find five-number summary • Min Q1 Med Q3 Max • draw box from Q1 to Q3 • draw median as center line in the box • extend whiskers to min & max

25. Modified boxplots display outliers fences mark off mild & extreme outliers whiskers extend to largest (smallest) data value insidethefence ALWAYS use modified boxplots in this class!!!

26. Inner fence Interquartile Range (IQR) – is the range (length) of the box Q3 - Q1 Q1 – 1.5IQR Q3 + 1.5IQR Any observation outside this fence is an outlier! Put a dot for the outliers.

27. Modified Boxplot . . . Draw the “whisker” from the quartiles to the observation that is within the fence!

28. Outer fence Any observation between the fences is considered a mild outlier. Q1 – 3IQR Q3 + 3IQR Any observation outside this fence is an extreme outlier!

29. Symmetrical boxplots Approximately symmetrical boxplot Skewed boxplot

30. Variable Type of variable Graph the heights of male students in your school Continuous numerical Histogram the income of adults in your city Discrete numerical Stem Plot the color of M&M candies selected at random from a bag Categorical Bar graph the number of TV’s in the homes of AP Stat students Discrete numerical Dot Plot the number of speeding tickets each student in AP Stat received Discrete numerical Dot Plot the birth weights of female babies born at a large hospital Continuous numerical Histogram the favorite movie type of AP Stat students by gender Categorical Bar graph – segmented or double the area code of an individual Categorical Bar graph the Math SAT Score for students at your school Discrete numerical Histogram Continuous numerical Cumulative frequency plot (ogive) the average number of text sent per month

31. How do you describe univariate data? Just CUSS and BS!

32. Center “the typical value” Mean Median Unusual Features Gaps Outliers

33. Shape single vs. multiple modes (unimodal, bimodal) symmetry vs. skewness

34. Unimodal Bimodal Multimodal Skew negatively (left) Symmetric Skew positively (right) Illustrated Distribution Shapes

35. Spread “how tightly values cluster around the center” Standard deviation Range IQR 5-number summary

36. And Be Specific!

37. Measures of Central Tendency • Median - the middle of the data; 50th percentile • Observations must be in numerical order • Is the middle single value if n is odd • The average of the middle two values if n is even NOTE:n denotes the sample size

38. Measures of Central Tendency parameter • Mean - the arithmetic average • Use m to represent a population mean • Use x to represent a sample mean statistic • Formula: S is the capital Greek letter sigma – it means to sum the values that follow

39. Measures of Central Tendency • Mode – the observation that occurs the most often • Can be more than one mode • If all values occur only once – there is no mode • Not used as often as mean & median

40. Suppose we are interested in the number of lollipops that are bought at a certain store. A sample of 5 customers buys the following number of lollipops. Find the median. The numbers are in order & n is odd – so find the middle observation. The median is 4 lollipops! 2 3 4 8 12

41. Suppose we have sample of 6 customers that buy the following number of lollipops. The median is … The numbers are in order & n is even – so find the middle two observations. The median is 5 lollipops! Now, average these two values. 5 2 3 4 6 8 12

42. Suppose we have sample of 6 customers that buy the following number of lollipops. Find the mean. To find the mean number of lollipops add the observations and divide by n. 2 3 4 6 8 12

43. What would happen to the median & mean if the 12 lollipops were 20? 5 The median is . . . 7.17 The mean is . . . What happened? 2 3 4 6 8 20

44. What would happen to the median & mean if the 20 lollipops were 50? 5 The median is . . . 12.17 The mean is . . . What happened? 2 3 4 6 8 50

45. Resistant - • Statistics that are not affected by outliers • Is the median resistant? YES NO • Is the mean resistant?

46. Look at the following data set. Find the mean. 22 23 24 25 25 26 29 30 Now find how each observation deviates from the mean. What is the sum of the deviations from the mean? Will this sum always equal zero? This is the deviation from the mean. YES 0

47. Look at the following data set. Find the mean & median. Mean = Median = 27 27 Create a histogram with the data. (use x-scale of 2) Then find the mean and median. Look at the placement of the mean and median in this symmetrical distribution. 21 23 23 24 25 25 26 26 26 27 27 27 27 28 30 30 30 31 32 32

48. Look at the following data set. Find the mean & median. Mean = Median = 28.176 25 Create a histogram with the data. (use x-scale of 8)Then find the mean and median. Look at the placement of the mean and median in this right skewed distribution. 22 29 28 22 24 25 28 21 25 23 24 23 26 36 38 62 23

49. Look at the following data set. Find the mean & median. Mean = Median = 54.588 58 Create a histogram with the data. Then find the mean and median. Look at the placement of the mean and median in this skewed left distribution. 21 46 54 47 53 60 55 55 60 56 58 58 58 58 62 63 64

50. Recap: • In a symmetrical distribution, the mean and median are equal. • In a skewed distribution, the mean is pulled in the direction of the skewness. • In a symmetrical distribution, you should report the mean! • In a skewed distribution, the median should be reported as the measure of center!