Data Toolbox

1. Chapter 1 Data Toolbox

2. Math Class Note-Taking Tips Write down the �title� of lesson. If you don�t know, ask me. Write down examples with math symbols step by step. Write down in your own words next to it.

3. More Note-Taking Tips Write down a �?� next to anything you don�t understand. Ask me about any �?�s� before you go. Before doing your homework, highlight in color what will give you the �big picture� in your notes.

4. Learning Objectives To distinguish between population and samples To recognize methods of sampling To identify a representative sample

5. 1-1 Populations and Samples Class Activity Why are surveys conducted? How are surveys done? What is the right amount of people to be surveyed? Has anyone been surveyed before?

6. Vocabulary Review Population: the whole group you are studying Sample: the specific part of the group you are studying Random Sample: gives every member of the population a fair chance of being chosen

7. Examples A scientist studies lions on a wildlife preserve to learn about the parenting habits of lions. Population? All lions Sample? -The lions on the preserve

8. More Examples The school librarian surveys 100 students about the types of books they prefer. Population? All students in the school Sample? -The 100 students who were surveyed

9. More Practice A restaurant manager uses comment cards to find out about customer satisfaction. Population? All customers Sample? -The customers who fill out the comment card

10. Random Samples A newspaper reporter is gathering responses from Riverside Middle School band students about the style of their uniforms. Which methods are random? A. The reporter questions only the students he knows personally. Not random B. The reporter questions every tenth student on an alphabetized list of students, starting with the first student on the list. -Not random

11. C. The reporter writes each student�s name on a card and puts all of the cards in a hat. He then questions the students whose names he draws. Random

12. Think and Discuss Give an example of a situation in which you would want to use a sample rather than poll the entire population. Explain why it might be difficult to obtain a purely random sample of a large population.

13. Learning Objectives To calculate mean, median, mode, and range To identify an outlier in a set of data To discover the effects an outlier has on mean, median, mode, and range

14. 1-2 Mean, Median, Mode, and Range Mode Median Mean Range Difference between the highest and lowest values Sum of the data values divided by the number of data items Middle value of numbers listed in order Value that occurs the most often

15. Mean 2, 1, 8, 0, 2, 4, 3, 4 Add #�s. Divide the sum by how many there are. 24 � 8 = 3 The mean is 3.

16. Median 2, 1, 8, 0, 2, 4, 3, 4 Least to greatest order Since there are two middle numbers, find the average of these two values. 2 + 3 = 5 5 � 2 = 2.5 The median is 2.5.

17. Mode 2, 1, 8, 0, 2, 4, 3, 4 Which number(s) occur the most? 2 and 4 each occur twice

18. Range 2, 1, 8, 0, 2, 4, 3, 4 Highest # - lowest # 8 � 0 = 8 The range is 8.

19. Outliers Outlier: a # much bigger or smaller than the others Find the outlier 35, 38, 27, 12, 30, 41, 31, 35 Which do you think the outlier will affect the most: the mean, median, and mode?

20. Effects of Outliers35, 38, 27, 12, 30, 41, 31, 35 Without the outlier Mean = 33.9 Median = 35 Mode = 35 With the outlier Mean = 31.1 Median = 33 Mode = 35

21. Think and Discuss Given the mean, median, and mode for a set of data, which measure MUST be an actual number in the set of data? Give an example of a data set with an outlier.

22. Learning Objectives To organize data into a stem and leaf plot To identify all parts of a stem and leaf plot

23. 1-3 Stem-and-Leaf Plots Stem-and-Leaf Plot: shows how often data values occur and how they are distributed The data shows the number of minutes students spent doing their homework. 38,48,45,32,45,36,22,21,35,45,47,26,43, 48,64

24. Step 1: List stems from least to greatest Step 2: List leaves for each stem from least to greatest. Step 3: Add a key and a title.

25. Minutes Doing Homework Stem Leaves

26. Practice The data shows the number of years coached by the top 15 coaches in all-time NFL coaching victories. 33, 40, 29, 33, 23, 22, 20, 21, 18, 23, 17, 15, 15, 12, 17

27. Number of Years Coached Stem Leaves

28. Think and Discuss Describe how you would show the number 4 on a stem-and-leaf plot? 89? 233?

29. Learning Objectives To interpret a bar graph to answer questions To construct a bar graph and double bar graph To identify the differences and similarities between bar graphs and double bar graphs

30. 1-4 Bar Graphs What do you think the difference is between a bar graph and a histogram?

31. Making a Double-Bar Graph The table shows the life expectancy of people in three Central American countries.

32. Bar graph vs. Histogram Shows categories Colors, cities Bars are not touching Shows intervals 1-10, 11-20 Bars are touching

33. Bar Graph Steps Step 1: Choose a scale Step 2: Draw a pair of bars in different colors Step 3: Label the axes and give the graph a title. Step 4: Make a key to show what each bar represents.

34. Practice

35. Think and Discuss Explain why you might use a double bar graph instead of two separate bar graphs to display data. Explain why you might use a horizontal bar graph instead of a vertical bar graph to display data.

36. Learning Objectives To organize data into a frequency table To use a frequency table to create a histogram To identify the steps required for a histogram

37. 1-3 Frequency Tables 1-4 Histograms Frequency table: organizes data into categories or groups (ready to make a histogram)

38. Organizing a Frequency Table The list shows the top 20 points scored at Buckeye in a football career 328, 206, 170, 158, 150, 148, 142, 142, 141, 140, 140, 138, 130, 128, 128, 126, 116, 114, 110, 110 Step 1: Choose your intervals Always include zero in your first interval Intervals of 50

40. Frequency Table Step 2: Find the number of data values in each interval. Write these numbers in the frequency column.

42. Frequency Table Step 3: Find the cumulative frequency Cumulative frequency: running total

44. Making a Histogram Step 1: Make a frequency table

45. Histogram Step 1: Choose scale for vertical axis Step 2: Draw a bar for each interval Step 3: Label the axes and give the graph a title

46. Practice

47. Think and Discuss Give an example of when you might use a frequency table to organize data. Describe the similarities and differences between a bar graph and a histogram.

48. Learning Objectives To interpret a circle graph to answer questions To approximate the percentages of sectors To choose which graph is most appropriate for a set of data

49. 1-5 Reading and Interpreting Circle Graphs Circle graph: aka pie chart, shows how the percentages of a set of data Sector: aka slice, each represents one part of the whole data

50. Example

51. About what % of people ordered cheese pizza? If 100 people took the survey, how many people ordered cheese? If 50 people took the survey, how many people ordered cheese? About what % ordered pepperoni?

52. More Practice

53. Did more teens pick skiing or snowboarding? About what % of teens picked skiing? How many teens chose skiing if 200 people took the survey? Which two sports combine for 50% of the population?

54. Bar Graph vs. Circle Graph The % of a nation�s electricity supply generated by several fuel sources The number of visitors to Arches National Park in each of the last 5 years The comparison between the time spent in math class and the total time spent in school each day

55. Think and Discuss Compare the use of circle graphs and bar graphs to display data. Describe two ways a circle graph can be used to compare data.

56. Learning Objectives To identify the steps in creating a box and whisker plot To interpret a box and whisker plot to answer questions To create a box and whisker plot

57. 1-6 Box and Whisker Plots Box and whisker plots: show the distribution of data by dividing it into 4 quartiles

58. Reading a Box and Whisker Plot

59. Making a Box and Whisker Plot FIVE NUMBER SUMMARY: Order from least to greatest Find min. and max. Find the median Find the median of lower half and upper half

60. Practice 26, 17, 21, 23, 19, 28, 17, 20, 29

61. Draw a number line. Decide the scale. Plot 5 points representing the five number summary.

62. More Practice 73,89,62,41,90,100, 116,82 Min= 1Q= Med.= 3Q= Max. =

63. One More Practice 101, 592, 450. 304, 123, 650, 545 Min.= 1Q= Med.= 3Q= Max.=

64. Think and Discuss What percent of the data is in within each quartile? Explain why you can�t find the mean or the mode by looking at the box and whisker plot. Does a box and whisker plot show how many items are in the data set?

65. Learning Objectives To create a line graph To use a line graph to estimate data To make a double line graph

66. 1-7 Line Graphs Line graph: shows change over time Ex. Growth of a cat over time

67. Making a Line Graph 1. Choose scale for axes (time goes on horizontal) 2. Plot points and connect 3. Label axes and give title

68. Practice

69. Estimate with a Line Graph How much do you think the cat will weigh at 16 months?

70. Double Line Graph Use two different colors for each set of data. Make a key

71. Normal Daily Temperatures in Alaska

72. Think and Discuss Describe how a line graph would look for a set of data that increases and decreases over time. Give an example of a situation that can be described by a double line graph and where the two sets intersect at least once.

73. Learning Objectives To create a scatter plot To interpret the relationship by looking at a scatter plot To provide examples of certain correlations

74. 1-8 Scatter Plots Scatter plot: represents a pair of data values, shows the relationship between two variables Ex. Age and IQ Correlation: extent of relationship

75. Birthday Month and Pets

76. Correlation Positive correlation: both sets of data increase at same time Negative correlation: one set increases while the other decreases No correlation: data sets show no pattern

77. Making a Scatter Plot Determine the scale and interval for each axis. Plot a point for each set of values. Label the axes and title the graph.

78. Math Scores vs. Shoe Size

79. Positive, Negative, or No Correlation Height and age Hand span and address Grade average and favorite color Date and temperature

80. Think and Discuss Describe the type of correlation you would expect between the number of absences in class and the grades. Give an example of two sets of data that shows a negative correlation. Then give an example that shows a positive correlation.

81. Scatter Plot Lab 1. A. On a piece of graph paper, draw the horizontal and vertical axes for a graph. B. Select 2 variables from the list below: Shoe size, length of forearm, month of birth, height, age in months, last 2 digits of phone #

82. Scatter Plot Lab C. Survey at least 10 people in class to find the values for these 2 variables. Write the information you get from each person as an ordered pair (Ex. Shoe size, last 2 digits of phone # could be 7, 31)

83. Scatter Plot Lab D. Label the axes of your graph with the variables. Then plot the data you gathered as points on the graph. Glue on the candy to mark your points.

84. Think and Discuss 1. Do the points on your graph form a pattern? Explain. 2. Do you have any point that does not fit your pattern? If so, how does this point compare to the other points? 3. Do the points appear to be almost in a straight line? If so describe the correlation (positive, negative, or none).

85. Try This Graph the ordered pairs below. How is the pattern in this graph similar or different from the pattern in the graph you made? (1,2), (2,2), (2,3), (3,4), (4,5), (5,5), (6,4), (7,6), (7,8), (8,7)

86. Learning Objectives To list the components that may make a graph misleading To interpret from a graph why it is misleading To explain why people may use misleading graphs

87. 1-9 Misleading Graphs Misleading: distorts the data in order to persuade Who do you think uses misleading graphs and why?

88. Example Career Builder Commercial

89. Ways to be Misleading Broken axis Not starting at zero Scale choice Not using equal intervals

96. Think and Discuss Describe what might indicate that a graph is misleading. Give an example of a situation in which a misleading graph might be used to persuade readers.

97. Studying for a Math Test Know how to distinguish between the various types of problems. Do 1 problem type from each section of the book chapter test. Show all steps and try to remember the differences between them.

98. Study Tips Go back to the sections where you�re having difficulty. Read through the examples. Reading a math book is not like reading a novel. It goes slowly. One example might take 20 minutes to understand.

99. Study Tips Don�t leave studying to the last minute. Ask questions before the test day. Work out as many problems as it takes for you to feel comfortable with the material.

100. Study Tips The day before the test, ask teacher to point out any major differences/similarities between types of problems. Get the phone # of someone in class you wouldn�t mind asking for help.

101. Study Tips If possible, form a small study group that meets periodically to study. Math is a cumulative subject. You REALLY need to understand today's material to understand the material the next day. Ask questions immediately in class as soon as you don't understand anything. Don't just "let it go".