1 / 42

Chapter 4: Collecting, Displaying, and Analyzing Data

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

sheila-eaton
Download Presentation

Chapter 4: Collecting, Displaying, and Analyzing Data

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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. 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

  6. 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

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

  8. 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.

  9. Try this one on your own… • 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.

  10. Example 2: Reading Stem-and-Leaf Plots • List the data values in the stem-and-leaf plot. 0 2 5 1 3 3 7 8 2 0 2 6 3 1 7 Key: 3 I 1 means 31 • Try this one on your own… 1 2 5 2 0 1 1 3 2 7 9 • 12, 15, 40, 41, 41, 52, 57, 59

  11. Example 3: Organizing Data in Stem-and-Leaf Plots • Use the data set on heights of trees in the U.S. (m) to make a stem-and-leaf plot.

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

  13. 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.

  14. 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.

  15. Section 4.3: Measures of Central Tendency

  16. 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

  17. 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 • 1st Quartile = 85 • 3rd 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 • 1st Quartile = (15 + 15) / 2 = 15 • 3rd Quartile = (17 + 18) / 2 = 17.5

  18. 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 • 1st Quartile: 15 • 3rd Quartile: 75 • 75, 61, 88, 79, 79, 99, 62, 77 • Range: 38 • 1st Quartile: 69 • 3rd Quartile: 83.5

  19. 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 • 1st Quartile: (21+21) / 2 = 21 • Median: 40 • 3rd Quartile: (48+49) / 2 = 48.5 • Largest: 62

  20. 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 • 1st Quartile: 16 • Median: 18 • 3rd Quartile: 21 • Largest: 25

  21. 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.

  22. 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.

  23. 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

  24. 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

  25. 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

  26. 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.

  27. Try this one on your own… • 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

  28. 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.

  29. Try this one on your own… • Make a line graph of the given data. • Use the graph to estimate Mr. Yi’s salary in 1992.

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

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

  32. 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.

  33. 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!

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

  35. Example 1: Making a Scatter Plot of a Data Set • 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.

  36. 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.

  37. Correlations

  38. 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

  39. 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

  40. 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

  41. Try this one on your own… • Use the date to predict how much a worker will earn in tips in 10 hours. • Approximately $24

More Related