1. Chapter 4: Collecting, Displaying, and Analyzing Data Regular Math

2. Section 4.1: Samples and Surveys Population – the entire group being studied Sample – part of the population Biased Sample – not a good representation Random Sample – every member has an equal chance Systematic Sample – according to a rule or formula Stratified Sample – at random from a randomly subgroup

3. Example 1: Identifying Biased Samples Identify the population and sample. Give a reason why the sample could be biased.  A radio station manager chooses 1500 people from the local phone book to survey about their listening habits. Population = people in the local area Sample = up to 1500 people that take the survey Biased = not everyone is in the phone book  An advice columnist asks her readers to write in with their opinions about how to hang the toilet paper on the roll. Population = readers of the column Sample = readers who wrote in Biased = only readers with strong opinions would write in  Surveyors in a mall choose shoppers to ask about their product preferences. Population = all shoppers at the mall Sample = people who are polled Biased = surveyors are more likely to approach people who look agreeable

4. Try these on your own… Identify the population and sample. Give a reason why the sample could be biased.  A record store manager asks customers who make a purchase how many hours of music they listen to each day. Population = record store customers Sample = customers who make a purchase Biased = Customers who make a purchase may be more interested in music than others who are in the store.  An eighth-grade student council member polls classmates about a new school mascot. Population = students in the school Sample = classmates Biased = She polls more eighth graders than students in other grades.

5. Sampling MethodHow Members Are Chosen RandomBy chance SystematicAccording to a rule or formula StratifiedAt random from randomly chosen subgroups

6. Example 2: Identifying Sampling Methods Identify the sampling method used.  An exit poll is taken of every tenth voter. systematic  In a statewide survey, five counties are randomly chosen and 100 people are randomly chosen from each county. stratified  Students in a class write their names on strips of paper and put them in a hat. The teacher draws five names. random

7. Try these on your own… Identify the sampling method used.  In a county survey, Democratic Party members whose names begin with the letter D are chosen. systematic  A telephone company randomly chooses customers to survey about its service. random  A high school randomly chooses three classes from each grade and then draws three random names from each class to poll about lunch menus. stratified

8. Section 4.2: Organizing Data Stem-and-Leaf Plot Back –to-Back Stem-and-Leaf Plot

9. Example 1: Organizing Data in Tables Use the given data to make a table.  Greg has received job offers as a mechanic at three airlines. The first has a salary range of $20,000- $34,000, benefits worth $12,000, and 10 days’ vacation. The second has 15 days’ vacation, benefits worth $10,500, and salary range of $18,000-$50,000. The third has benefits worth $11,400, a salary range of $14,000-$40,000, and 12 days’ vacation. Job 1Job 2Job 3 Salary Range $20,000 - $34,000 $18,000 - $50,000 $14,000 - $40,000 Benefit s $12,000$10,500$11,400 Vacatio n Days 101512

10. Try this one on your own… DayTo SchoolTo Home Monday7 min9 min Tuesday5 min9 min Wednesday8 min7 min Use the given data to make a table.  Jack timed his bus rides to and from school. On Monday, it took 7 minutes to get to school and 9 minutes to get home. On Tuesday, it took 5 minutes and 9 minutes respectively, and on Wednesday, it took 8 minutes and 7 minutes.

11. Example 2: Reading Stem-and-Leaf Plots List the data values in the stem-and-leaf plot. 02 5 13 3 7 8 20 2 6 31 7 Key: 3 I 1 means 31 Try this one on your own… 1 2 5 20 1 1 32 7 9  12, 15, 40, 41, 41, 52, 57, 59

12. Example 3: Organizing Data in Stem-and- Leaf Plots Ash 47Elm 38Red Maple 55 Beech 40Grand Fir 77Sequoia 84 Black Maple 40Hemlock 74Spruce 63 Cedar 67Hickory 58Sycamore 40 Cherry 42Oak 61Western Pine 48 Douglas Fir 91Pecan 44Willow 35 Use the data set on heights of trees in the U.S. (m) to make a stem-and-leaf plot.

13. Try this one on your own… Use the data on top speeds of animals (mi/h) to make a stem-and-leaf plot. Cheetah64Elk45 Wildebeest61Coyote43 Lion50Gray Fox42

14. Example 4: Organizing Data in Back-to- Back Stem-and-Leaf Plots Use the given data on Super Bowl scores, 1990- 2000, to make a back-to-back stem-and-leaf plot. 19901991199219931994199519961997199819992000 Winning5520375230492735313423 Losing1019241713261721241916

15. Try this one on your own… Use the data on US. Representatives for Selected States, 1950 and 2000, to make a back-to-back stem-and-leaf plot. ILMAMINYPA 19502514184331 20001910152919

16. Section 4.3: Measures of Central Tendency DefinitionUse to Answer Mean – the sum of the values, divided by the number of values “What is the average?” “What single number best represents the data?” Median – the middle number in an ordered set of data “What is the halfway point of the data?” Mode – the value or values that occur most often “What is the most common value?”

17. Section 4.4: Variability Variability – how spread out the data is Range – largest number minus the smaller number Quartile – divide data parts into four equal parts Box-and-Whisker Plot – shows the distribution of data

18. Example 1: Finding Measures of Variability Find the range and the first and third quartiles for each data set.  85, 92, 78, 88, 90, 88, 89 78, 85, 88, 88, 89, 90, 92 Range: 92-78 = 14 1 st Quartile = 85 3 rd Quartile = 90  14, 12, 15, 17, 15, 16, 17, 18, 15, 19, 20, 17 12, 14, 15, 15, 15, 16, 17, 17, 17, 18, 19, 20 Range: 20-12 = 8 1 st Quartile = (15 + 15) / 2 = 15 3 rd Quartile = (17 + 18) / 2 = 17.5

19. Try these on your own… Find the range and the first and third quartiles for each data set.  15, 83, 75, 12, 19, 74, 21 Range: 71 1 st Quartile: 15 3 rd Quartile: 75  75, 61, 88, 79, 79, 99, 62, 77 Range: 38 1 st Quartile: 69 3 rd Quartile: 83.5

20. Example 2: Making a Box-and-Whisker Plot Use the given data to make a box-and- whisker plot.  22, 17, 22, 49, 55, 21, 49, 62, 21, 16, 18, 44, 42, 48, 40, 33, 45 Find the smallest value, first quartile, median, third quartile, and largest value.  Smallest: 16  1 st Quartile: (21+21) / 2 = 21  Median: 40  3 rd Quartile: (48+49) / 2 = 48.5  Largest: 62

21. Try this one on your own… Use the given data to make a box-and- whisker plot.  21, 25, 15, 13, 17, 19, 19, 21 Smallest: 13 1 st Quartile: 16 Median: 18 3 rd Quartile: 21 Largest: 25

22. Example 3: Comparing Data Sets Using Box-and-Whisker Plots These box-and-whisker plots compare the number of home runs Babe Ruth hit during his 15-year career from 1920 to 1934 with the number Mark McGwire hit during the 15 years from 1986 to 2000.  Compare the medians and ranges.  Compare the ranges of the middle half of the data for each.

23. Try these on your own… These box-and-whisker plots compare the ages of the first ten U.S. presidents with the ages of the last ten presidents (through George W. Bush) when they took office.  Compare the medians and ranges.  Compare the differences between the third quartile and first quartile for each.

24. Section 4.5: Displaying Data Bar Graph – display data that can be grouped in categories Frequency Table – use with data that is given in list Histogram – type of bar graph; groups by using intervals Line Graph – show trends or to make estimates

25. Example 1: Displaying Data in a Bar Graph Organize the data into a frequency table and make a bar graph.  The following are the ages when a randomly chosen group of 20 teenagers received their driver’s licenses: 18, 17, 16, 16, 17, 16, 16, 16, 19, 16, 16, 17, 16, 17, 18, 16, 18, 16, 19, 16 Age License Received 16171819 Frequency11432

26. Try this one on your own… Organize the data into a frequency table and a bar graph.  The following data set reflects the number of hours of television watched every day by members of a sixth- grade class: 1,1,3,0,2,0,5,3,1,3 HoursFrequency 02 13 21 33 40 51

27. Example 2: Displaying Data in a Histogram John surveyed 15 people to find out how many pages were in the last book they read. Use the data to make a histogram.  368, 153, 27, 187, 240, 636, 98, 114, 64, 212, 302, 144, 76, 195, 200 Make a frequency table first. Then, use intervals of 100 to make a histogram. PagesFrequency 0-99 100-199 200-299 300-399 400-499 500-599 600-699

28. Try this one on your own… DollarsFrequency 0-0.99 1.00 – 1.99 2.00 – 2.99 3.00 – 3.99 Jimmy surveyed 12 children to find out how much money they received from the tooth fairy. Use the data set to make a histogram.  0.35, 2.00, 0.75, 2.50, 1.50, 3.00, 0.25, 1.00, 1.00, 3.50, 0.50, 3.00

29. Example 3: Displaying Data in a Line Graph Make a line graph of the given data. Use the graph to estimate the number of polio cases in 1993. YearNumber of Polio Cases Worldwide 197549,293 198052,552 198538,637 199023,484 19957,035 20002,880

30. Try this one on your own… YearSalary ($) 198542,000 199049,000 199558,000 200069,000 Make a line graph of the given data. Use the graph to estimate Mr. Yi’s salary in 1992.

31. Section 4.6: Misleading Graphs and Statistics Explain why each graph is misleading.

32. Try this one on your own… Explain why the graphs are misleading.

33. Example 2: Identifying Misleading Statistics Explain why each statistic is misleading.  A small business has 5 employees with the following salaries: $90,000 (owner); $18,000; $22,000; $20,000; $23,000. The owner places an ad that reads: “Help Wanted – average salary $34,600” Only one person in the company makes more than $23,000 and that is the owner. It is not likely that a new person’s salary would be close to $34,600.  A market researcher randomly selects 8 people to focus-test three brands, labeled A, B, and C. Of these, 4 chose brand A, 2 chose brand B, and 2 chose brand C. An ad for brand A states: Preferred 2 to 1 over leading brands!” The sample size is too small. The researcher needs to ask more people to get a true representation.  The total revenue at Worthman’s for the three-month period from June 1 to September 1 was $72,000. The total revenue at Meilleure for the three-month period from October 1 to January 1 was $108,000. They are comparing two different times of the year.

34. Try these on your own… Explain why each statistic is misleading.  Sam scored 43 goals for his soccer team during the season, and Jacob scored only 2.  Four out of five dentists surveyed preferred Ultraclean toothpaste.  Shopping at Save-a-Lot can save you up to $100 a month!

35. Section 4.7: Scatter Plots Scatter Plots – show relationships between two data sets

36. Example 1: Making a Scatter Plot of a Data Set CompoundZIAAverage Effects Zinc Gluconate100Reduced cold 7 days Zinc Gluconate44Reduced cold 4.8 days Zinc Orotate0None Zinc Gluconate25Reduced cold 1.6 days Zinc Gluconate13.4None Zinc Aspartate0None Zinc Acetate-tartarate-glycine-55Increased cold 4.4 days Zinc Gluconate-11Increased cold 1 day A scientist studying the effects of zinc lozenges on colds has gathered the following data. Zinc ion availability (ZIA) is a measure of the strength of the lozenge. Use the data to make a scatter plot.

37. Try this one on your own… Use the given data to make a scatter plot of the weight and height of each member of a basketball team. Height (in)Weight (lb) 71170 68160 70175 73180 74190

38. Correlations

39. Example 2: Identifying the Correlation of Data Do the data sets have positive, a negative, or no correlation?  The population of a state and the number of representatives positive  The number of weeks a movie has been out and weekly attendance negative  A person’s age and the number of siblings they have No correlation

40. Try these on your own… Do the data sets have a positive, negative, or no correlation?  The size of a jar of baby food and the number of jars a baby eats negative  The speed of a runner and the number of races she wins positive  The size of a person and the number of fingers he has No correlation

41. Example 3: Using a Scatter Plot to Make Predictions Use the data to predict the exam grade for a student who studies 10 hours per week.  About 95 Hours StudiedExam Grade 580 995 375 1298 170

42. Try this one on your own… Use the date to predict how much a worker will earn in tips in 10 hours.  Approximately $24 HoursTips ($) 412 820 37 27 1126