1. 1CONFIDENTIAL Data & Graphs Review

2. CONFIDENTIAL2 Frequency Tables Statistics involves collecting, organizing, analyzing, and presenting data. Data are pieces of information that are often numerical. A frequency table shows the number of pieces of data that fall within given intervals.

3. CONFIDENTIAL3 Make a Frequency Table Example: The number of points scored by major league soccer teams in a recent season is shown. Major League Soccer Points Scored 53263545 42531436 27454723

4. CONFIDENTIAL4 Make a Frequency Table Step 1: Choose an appropriate scale and interval for the data Scale:1 to 60 Interval:15 The scale includes all of the data, the least number and the greatest The interval separates the scale into equal parts.

5. CONFIDENTIAL5 Make a Frequency Table Step 2: Draw a table with three columns and label the columns Points, Tally, and Frequency Step 3: In the first column, list the intervals. In the second column, tally the data. In the third column, add the tallies. Major League Soccer Points Scored, 2001 season PointsTallyFrequency 1-15I1 16-30III3 31-45IIII5 46-60III3 Some frequency tables may not have scales and intervals

6. CONFIDENTIAL6 Make a Frequency Table Make a frequency table of the data shown in the table. Surprise Quiz Scores 99 83 92 52 75 90100 65 80 85 53 80 75 85 85 70 75 90 95 75 Your Turn Surprise Quiz Scores PointsTallyFrequency 51-60II2 61-70II2 71-80IIII I6 81-90IIII I6 91-100IIII4

7. CONFIDENTIAL7 Line Graphs A line graph is used to show how a set of data changes over a period of time. Number of Coasters The scale and interval are also shown on the vertical axis. A line graph also has titles and labels The categories are written on the horizontal axis. Each frequency is shown using a point.

8. CONFIDENTIAL8 Make & Interpret a Line Graph Example: Make a line graph of the data at the left. Then describe the change in the number of tornadoes from 2001 to 2003. Step 1; Decide on the scale and the interval. The data includes numbers from 941 to 1,424. The scale is 900 to 1,500 and the interval is 100. U.S.Tornadoes YearTornadoes 19981,424 19991,343 20001,071 20011,216 2002941 20031,246

9. CONFIDENTIAL9 Make & Interpret a Line Graph Step 2: Label the horizontal and vertical axes. Step 3: Draw and connect the points for each year. Each point shows the number of tornadoes in that year. Step 4: Label the graph with a title. The number of tornadoes decreased from 2001 to 2002 and then increased from 2002 to 2003. Tornadoes

10. CONFIDENTIAL10 Make & Interpret a Line Graph Make a line graph of the data. Then describe the change from 1960 to 1995. U.S. Water Consumption YearWater consumed per day (billion gallons) 196061 196577 197087 197596 1980100 198592 199094 1995100 Your Turn Water consumption increased from 1960 to 1995, with a slight dip in use between 1980 and 1995.

11. CONFIDENTIAL11 Bar Graphs A bar graph is used to compare data. Revenue $ millions Time Sales of toys The scale is written on the vertical axis On this scale, the interval is 50 The categories are written on the horizontal axis. The height of each bar represents the frequency The title and label describe the data

12. CONFIDENTIAL12 Make & Interpret a Bar Graph Example: Make a vertical bar graph of the data. Compare the number of students who scored a B to the number who scored a C. Step 1: Decide on the scale and interval. The data includes numbers from 2 to 13. So, a scale from 0 to 14 and an interval of 2 is reasonable. Math Scores GradeFrequency A10 B13 C7 D2

13. CONFIDENTIAL13 Make & Interpret a Bar Graph Step 2: Label the horizontal and vertical axes. Step 3: Draw bars for each grade. The height of each bar shows the number of students earning that grade. Step 4: Label the graph with a title. About twice as many students scored a B than a C.

14. CONFIDENTIAL14 Make & Interpret a Bar Graph Make a vertical bar graph of the data. Compare the time it takes for a rabbit to be born to the time it takes for a camel to be born. Gestation of selected animals AnimalsGestation period (days) Squirrel44 Rabbit31 Puma90 Moose240 Kangaroo36 camel406 Your Turn It takes about 13 times as many days for a camel to be born as it does for a rabbit to be born.

15. CONFIDENTIAL15 Circle Graphs A circle graph is used to compare parts of a whole. Analyze data by comparing the size of the sections of the circle. One can compare the percents to analyze the data as well. The pie-shaped sections show the groups. The percents add up to 100% The interior of the circle represents a set of data.

16. CONFIDENTIAL16 Circle Graphs The circle graph shows which method of transportation students use to get to Martin Luther King, Jr. Middle School. 1.Which method of transportation do most students use? 2.How does the number of students who ride a moped to school compare to the number of students who take the bus? Your Turn 1)Bus 2)About five times the number of students ride the bus.

17. CONFIDENTIAL17 Stem & Leaf Plots In a stem-and-leaf plot, the data is ordered from least to greatest and is organized by place value. Step 1: Order the data from least to greatest 56 60 62 67 68 68 69 70 70 70 71 72 76 76 78 82 83 84 88 93 97 Step 2: Draw a vertical line and write the tens digits from least to greatest to the left of the line. These digits form the stems. Since the least value is 56 and the greatest value is 97, the stems are 5, 6, 7, 8, and 9. NCAA Division 1 Women’s Basketball Points Scored by Winning Teams, 1982-2002 76 70 56 70 60 68 71 69 97 76 78 70 93 68 72 67 88 84 83 62 82

18. CONFIDENTIAL18 Stem & Leaf Plots Step 3: Write the units digits in order to the right of the line with the corresponding stem. The units digits form the leaves. Stem Leaf 56 6 7 8 9 0 2 7 8 8 9 0 0 0 1 2 6 6 8 2 3 4 8 3 7 7 6 points key In this data, the tens digit forms the stem. The ones digit of the data form the leaves. Always write each leaf even if it repeats.

19. CONFIDENTIAL19 Stem & Leaf Plots Make a stem-and-leaf plot for the data in the table. Average July Highs ( o F) for selected European cities 69 72 71 73 76 60 81 67 78 89 74 75 74 66 79 73 88 77 Your Turn Stem Leaf 6 7 8 6 7 9 0 1 2 3 3 4 4 5 6 7 8 9 1 8 9 7 8 = 78

20. CONFIDENTIAL20 Making Predictions & Interpreting Graphs Line graphs are often used to predict future events because they show trends over time. Example: You can predict the average temperature for Miami in February by the trend in the line graph.

21. CONFIDENTIAL21 Making Predictions & Interpreting Graphs The graph shows the number of participants in bowling from 1975 to 2000. What does the graph tell you about the popularity of bowling? Your Turn The popularity of bowling dropped off in mid-nineteen eighties, but it has since recovered and grown in popularity.

22. CONFIDENTIAL22 Mean The mean of a set of data is the sum of the data divided by the number of pieces of data. Example: data set : 8, 7, 9, 6, 10 Mean = 8 + 7 + 9 + 6 + 10 = 40 = 8 5 5

23. CONFIDENTIAL23 Determine how Outliers affect Mean A set of data may contain a value much higher or lower than the other values. This value is called outlier. Outliers can significantly affect the mean. Example: data set : 80, 81, 40, 77, 82 Mean with outlier = 80 + 81 + 40 + 77 + 82 = 360 = 72 5 Mean without outlier = 80 + 81 + 77 + 82 = 320 = 80 4

24. CONFIDENTIAL24 Median, Mode, and Range The median of a set of data is the middle number of the ordered data, or the mean of the middle two numbers. Examples: –data set: 3, 4, 8, 10, 12 -> median: 8 –data set: 2, 4, 6, 8, 11, 12 -> median: 6 + 8 = 7 2

25. CONFIDENTIAL25 Median, Mode, and Range The mode of a set of data is the number or numbers that occur most often. Examples: –data set: 12, 23, 28, 28, 32, 46, 46 -> modes: 28 and 46

26. CONFIDENTIAL26 Median, Mode, and Range The range of a set of data is the difference between the greatest and the least values of the set. Examples: –data set: 125, 45, 67, 150, 32, 12 –The greatest value is 150. –The least value is 12. –So, the range is 150 – 12 or 138.

27. CONFIDENTIAL27 Median, Mode, and Range Concept Summary MeasureBest Used to describe the data when… MeanThe data set has no very high or low numbers. MedianThe data set has some high or low numbers and most of the data in the middle are close in value. ModeThe data set has many identical numbers.

28. CONFIDENTIAL28 Median, Mode, and Range What are the mean, median, mode, and range of the temperature data 64 0, 70 0, 56 0, 58 0, 60 0, and 70 0. Mean: 64 + 70 + 56 + 58 + 60 + 70 = 378 = 63 0 6 Median: 56, 58, 60, 64, 70, 70 Mode: 70 0 Your Turn 60 + 64 = 124 = 62 0 2 2 There is an even number of data values. So, to find the median, find the mean of the two middle numbers.

29. CONFIDENTIAL29 Let us take a break!

30. CONFIDENTIAL30 Jig-saw puzzle http://www.thekidzpage.com/onlinejigsawpuzzles/jigsaw- puzzles/12-piece-jigsaw/05-04-06-kitten.htmlhttp://www.thekidzpage.com/onlinejigsawpuzzles/jigsaw- puzzles/12-piece-jigsaw/05-04-06-kitten.html

31. CONFIDENTIAL31 Box & Whisker Plots A Box-and-whisker plot is a way to show how data are clustered or spread out. Example: The monthly mean temperatures for Burlington, Vermont, are shown. Monthly Normal Temperatures for Burlington, VT MonthJFMAMJJASOND Temp ( 0 F) 161831445665716859483723

32. CONFIDENTIAL32 Box & Whisker Plots Step 1: Write the data from least to greatest. 16 18 23 31 37 44 48 56 59 65 68 71 Step 2: Draw a number line that includes all of the data. 15 2025 30 35 4045 50 55 6065 70 75 Step 3: Mark the least and greatest as the lower extreme and upper extreme. Find and label the median. 15 2025 30 35 4045 50 55 6065 70 75 Lower ExtremeUpper Extreme Median

33. CONFIDENTIAL33 Box & Whisker Plots Step 4: The median of a data set separates the set in half. Find the medians of the lower and upper halves. 16 18 23 31 37 44 48 56 59 65 68 71 15 2025 30 35 4045 50 55 6065 70 75 Lower Extreme Upper Extreme Median 23 + 31 = 27 2 Median 59 + 65 = 62 2 Label these values as lower quartile and upper quartile. Draw a box around the quartile values, and whiskers that extend from each quartile to the extreme data points. Upper Quartile Lower Quartile

34. CONFIDENTIAL34 Box & Whisker Plots Draw a Box-and-whisker plot for the set of data below. Baseball Games won by Teams in National League, 2002 95947967659585737269659786858276 Your Turn 65 6769 71 73 7579 81 83 8587 89 91 Lower Extreme Upper Extreme Median Upper Quartile Lower Quartile 939597

35. CONFIDENTIAL35 Assessment 1) Make a frequency table for the set of data. Number of siblings 31 2 1 3 1 0 4 1 0 2 1 2 1 0 3 1 0 Number of siblings TallyFrequency 0IIII4 1IIII II7 2III3 3 3 4I1

36. CONFIDENTIAL36 Assessment 2) Make a line graph for the set of data. Zoo Visitors YearVisitors 200012,300 200113,400 200215,900 200315,100 200416,200

37. CONFIDENTIAL37 Assessment 3) Name two muffins that together are preferred by half the people surveyed. Banana and cinnamon

38. CONFIDENTIAL38 Assessment 4) Describe the trend in the winning times. Predict the winning time in 2006. The winning times are decreasing.

39. CONFIDENTIAL39 Assessment 5) Make a stem-and-leaf plot for the set of data. 83, 72, 95, 64, 90, 88, 78, 84, 61, 73 Stem Leaf 6 7 8 1 4 2 3 8 3 4 8 7 2 = 72 9 0 5

40. CONFIDENTIAL40 Assessment 6) Find the mean for the set of data. 23, 34, 29, 36, 18, 22, 27 27

41. CONFIDENTIAL41 Assessment 7) Find the median, mode, and range for the set of data. 21, 23, 27, 30 25 None 9

42. CONFIDENTIAL42 Assessment 8) Which graph would you show to a telephone customer? Explain. Graph A; the calls look cheaper

43. CONFIDENTIAL43 Great Job! See you in the Session!