Chapter 1: Exploring Data 1.1 – Displaying Distributions with Graphs

1. Chapter 1: Exploring Data 1.1 – Displaying Distributions with Graphs

2. Types of Graphs: Categorical Quantitative Dotplot Bar Chart Stemplot Pie Chart Histogram Ogive Time Plot

3. Count categories Bar graph: Displays categorical variables Title How to construct a bar graph: Step 1: Label your axes and title graph Step 2: Scale your axes Step 3: Leave spaces between bars

4. Legend = Count = categories Side-by-Side bar graph: Compares two variables of one individual Title

5. Example #1 The table shows results of a poll asking adults whether they were looking forward to the Super Bowl game, the commercials, or didn’t plan to watch. Construct a side-by-side bar chart for their preference based on gender. Note any trends that appear.

6. Reason Looking Forward to Super Bowl 300 = Game 250 = Commercials 200 150 = Won’t Watch 100 50 Female Male Males overwhelmingly watch the Super Bowl for the game, where women seem mixed as to why they want to watch it.

7. Describing Quantitative Distributions: When describing a Graph -- CUSS C - Center Average value, add up then divide by # Mean: Most frequent number. There can be many modes Mode: Number in the center when data is lined up Median:

8. Calculator Tip: To calculate mean and median Stat – edit – type in data – exit Stat – CALC – 1-Var Stats - L1

9. Describing Quantitative Distributions: When describing a Graph -- CUSS U - Unusual points Any data points that stand out as different Don’t call them outliers yet!

10. Describing Quantitative Distributions: When describing a Graph -- CUSS S - Shape Fold in half, it matches up Symmetric: Special Case, don’t say yet! Bell/Normal: All the same frequencies Uniform:

11. S - Shape One peak in the data Unimodal: Two peaks in the data Bimodal:

12. S - Shape Gaps: Space between the data Several data points grouped together Cluster:

13. S - Shape Skewed Right: Unusual point to the right Skewed Left: Unusual point to the left

14. Describing Quantitative Distributions: When describing a Graph -- CUSS S - Spread Distance between largest and smallest values. Range = Maximum - Minimum Range: Homogeneous: Data is all in a similar space (small spread)

16. # range Dotplot: Dots are used to keep count of the frequency of each number How to construct a dotplot: Step 1: Label your axis and title your graph. Step 2: Mark a dot above the corresponding value TITLE

17. Example #2 The data below give the number of hurricanes classified as major hurricanes in the Atlantic Ocean each year from 1944 through 2006, as reported by NOAA. • Make a dotplot of the data.

18. Number of Hurricanes Classified as a Major Hurricane (1944-2006) b. Describe what you see in a few sentences.

19. A dotplot is a simple display. It just places a dot along an axis for each case in the data. • The dotplot to the right shows Kentucky Derby winning times, plotting each race as its own dot. • You might see a dotplot displayed horizontally or vertically.

20. Guidelines for constructing Stemplots (stem and leaf) 1. Put data in order from smallest to largest • 2. Separate each value in a STEM and LEAF • The leaf is a single digit and it is the rightmost digit of the number. The stem will consist of everything else to the left of the leaf 3. Stems go in a vertical column from small to large and a vertical line is drawn to the right of the stems 4. Leaves are written to the right of their stems from small to large.

21. Back-to-Back Stemplots To compare two different sets of data Split Stemplots To spread out the data to see more trends if they are grouped together. Leaves will split from 0-4 and 5-9.

22. Example #3 The data below give the amount of caffeine content (in milligrams) for an 8-ounce serving of popular soft drinks. • Construct stemplot. • Construct a split stemplot.

23. Caffeine per 8oz of soda a. 1 2 3 4 5 5 6 0 3 3 3 4 4 5 5 6 6 7 7 7 8 8 8 8 8 9 9 1 1 3 5 5 5 6 7 7 7 8 3 3 7 7 Key: 1 5 = 15mill b. 1 2 2 3 3 4 4 5 5 6 0 3 3 3 4 4 5 5 6 6 7 7 7 8 8 8 8 8 9 9 1 1 3 5 5 5 6 7 7 7 8 3 3 7 7 c. Differences?

24. www.whfreeman.com/tps3e 1-Var Stats

26. Most people believe that you need to drink coffee or an energy drink to get good “buzz” off of the caffeine. Below is a table with common caffeine levels of tea, coffee, and energy drinks. Coffee Energy Drink d. Make a back-to-back stemplot. Comment on the difference in caffeine levels between coffee and energy drinks.

27. Coffee Energy Drink 0 5 5 3 3 5 3 0 0 0 0 8 0 9 4 4 5 6 7 8 9 10 11 12 13 14 15 16 3 0 0 0 5 0 0 4 0 Key: 1 5 = 15mg

28. http://www.cspinet.org/new/cafchart.htm

29. http://www.cspinet.org/new/cafchart.htm

30. 562 56.2 5.62 562 56 2 56 2 56 2 5 6 50 2 5 0 0 2

31. Back-to-Back Stemplots To compare two different sets of data 565 562 572 580 577 565 5 2 56 5 57 2 7 0 58

32. Split Stemplots To spread out the data to see more trends if they are grouped together. Leaves will split from 0-4 and 5-9. 565 562 572 580 577 565 2 56 5 56 5 57 2 57 7 0 58

33. Count towards median median Count towards median

34. Sort values from smallest to largest Calculator Tip: Stat – Edit – type in data – exit Stat – SortA – L1

35. Clearing Lists Calculator Tip: All Lists: Mem – ClrAllLists – Enter One List: Stat – Edit – Highlight List name – Clear

36. Deleted a list? Calculator Tip: STAT – SetUpEditor – Enter

37. Save a list? Calculator Tip: L1 – STO – Any name or Letter To Retrieve later: 2nd – List

38. Remove a number from list? Calculator Tip: Line up number you want to delete, hit DEL

39. Histogram: 1. Divide the range of data into classes of equal width. 2. Count the number of observations in each class. Ensure no one number falls into two classes 3. Label and scale the axes and title your graph. 4. Draw a bar that represents the count in each class. The base of a bar should cover its class, and the bar height is the class count. Leave no horizontal space between the bars unless the class is empty.

40. Make a histogram. Pg. 59 Calculator Tip: Stat – Edit – type in data – exit StatPlot – 1 – On – histogram – L1 – Freq 1 Zoom – ZoomStat (#9)

41. To adjust the classes: Window: Xmin: Lowest value Xmax: Highest value Xscl: Scale on x-axis (width of bars) Ymin: -0.2 typically Ymax: Highest frequency rate (height of bars) Yscl: Scale on y-axis Ymax Yscl Ymin Xscl Xmax Xmin

42. Ex. #4: Describe the distribution of the graph. C: 4-5 words U: 12 words S: Unimodal, slight skew right S: 1 to 12 Range = 11

43. Example#5: An executive finds the subscriptions (in millions of people) of the 20 leading American magazines is as follows: Make a histogram for the number of subscriptions in intervals of 2 (million) compared to the frequency of that number. Then describe the graph.

44. Circulation in millions of people of American Magazines 8 7 6 5 4 3 2 1 Frequency 2 4 6 8 10 12 14 16 18 20 Circulation (in millions) Describe the features of the graph in detail. C: mean = 6 .825, median = 5.35 U: 17.1 & 17.9 S: Skewed to the right, unimodal S: 2.8 to 17.9, range of 15.1

45. Height of NBA Players

46. http://bcs.whfreeman.com/tps3e Page 50: applets: One-variable Statistical calculator • How do you determine how many classes to make? • When is it good to split the stems on a stemplot?

47. HW

48. Day 3 1.1 & 1.2

49. Relative Cumulative Frequency Graph (Ogive): Shows relative standing of an observation

50. Example #6: The President of the United States has to be at least 35 years old and be born in America. Below is an ogive showing the relative cumulative frequency of the previous presidents that were inaugurated. • What percent of presidents were younger than 60? 80%