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Review Slides

Review Slides. Example 1 . Two dice were thrown 10 times and their scores were added together and recorded. Find the mean and range for this data. 7, 5, 2, 7, 6, 12, 10, 4, 8, 9. Mean = 7 + 5 + 2 + 7 + 6 + 12 + 10 + 4 + 8 + 9. 10. = 70. 10. = 7.

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Review Slides

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  1. Review Slides

  2. Example1. Two dice were thrown 10 times and their scores were added together and recorded. Find the mean and range for this data. 7, 5, 2, 7, 6, 12, 10, 4, 8, 9 Mean = 7 + 5 + 2 + 7 + 6 + 12 + 10 + 4 + 8 + 9 10 = 70 10 = 7 Median, Quartiles, Inter-Quartile Range and Box Plots. Measures of Spread Remember: The range is the measure of spread that goes with the mean. Range = 12 – 2 = 10

  3. Median, Quartiles, Inter-Quartile Range and Box Plots. Measures of Spread The range is not a good measure of spread because one extreme, (very high or very low value) can have a big affect. The measure of spread that goes with the median is called the inter-quartile range and is generally a better measure of spread because it is not affected by extreme values. A reminder about the median

  4. Averages (The Median) The median is the middle value of a set of data once the data has been ordered. Example 1.Robert hit 11 balls at Grimsby driving range. The recorded distances of his drives, measured in yards, are given below. Find the median distance for his drives. 85, 125, 130, 65, 100, 70, 75, 50, 140, 95, 70 50, 65, 70, 70, 75, 85, 95, 100, 125, 130, 140 Ordered data Single middle value Median drive = 85 yards

  5. Averages (The Median) The median is the middle value of a set of data once the data has been ordered. Example 1.Robert hit 12 balls at Grimsby driving range. The recorded distances of his drives, measured in yards, are given below. Find the median distance for his drives. 85, 125, 130, 65, 100, 70, 75, 50, 140, 135, 95, 70 50, 65, 70, 70, 75, 85, 95, 100, 125, 130, 135, 140 Two middle values so take the mean. Ordered data Median drive = 90 yards

  6. Example1. Two dice were thrown 10 times and their scores were added together and recorded. Find the mean and range for this data. 7, 5, 2, 7, 6, 12, 10, 4, 8, 9 Mean = 7 + 5 + 2 + 7 + 6 + 12 + 10 + 4 + 8 + 9 10 = 70 10 = 7 Median, Quartiles, Inter-Quartile Range and Box Plots. Measures of Spread Remember: The range is the measure of spread that goes with the mean. Range = 12 – 2 = 10

  7. Median, Quartiles, Inter-Quartile Range and Box Plots. Measures of Spread The range is not a good measure of spread because one extreme, (very high or very low value) can have a big affect. The measure of spread that goes with the median is called the inter-quartile range and is generally a better measure of spread because it is not affected by extreme values. A reminder about the median

  8. Averages (The Median) The median is the middle value of a set of data once the data has been ordered. Example 1.Robert hit 11 balls at Grimsby driving range. The recorded distances of his drives, measured in yards, are given below. Find the median distance for his drives. 85, 125, 130, 65, 100, 70, 75, 50, 140, 95, 70 50, 65, 70, 70, 75, 85, 95, 100, 125, 130, 140 Ordered data Single middle value Median drive = 85 yards

  9. Averages (The Median) The median is the middle value of a set of data once the data has been ordered. Example 1.Robert hit 12 balls at Grimsby driving range. The recorded distances of his drives, measured in yards, are given below. Find the median distance for his drives. 85, 125, 130, 65, 100, 70, 75, 50, 140, 135, 95, 70 50, 65, 70, 70, 75, 85, 95, 100, 125, 130, 135, 140 Two middle values so take the mean. Ordered data Median drive = 90 yards

  10. Q2 Q1 Q3 Upper Quartile = 9 Lower Quartile = 5½ Median = 8 Finding the median, quartiles and inter-quartile range. Example 1: Find the median and quartiles for the data below. 12, 6, 4, 9, 8, 4, 9, 8, 5, 9, 8, 10 Order the data 4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12 Inter-Quartile Range = 9 - 5½ = 3½

  11. Q2 Q3 Q1 Upper Quartile = 10 Lower Quartile = 4 Median = 8 Finding the median, quartiles and inter-quartile range. Example 2: Find the median and quartiles for the data below. 6, 3, 9, 8, 4, 10, 8, 4, 15, 8, 10 Order the data 3, 4, 4, 6, 8, 8, 8, 9, 10, 10, 15, Inter-Quartile Range = 10 - 4 = 6

  12. Discuss the calculations below. Battery Life: The life of 12 batteries recorded in hours is: 2, 5, 6, 6, 7, 8, 8, 8, 9, 9, 10, 15 Mean = 93/12 = 7.75hours and the range = 15 – 2 = 13 hours. 2, 5, 6, 6, 7, 8, 8, 8, 9, 9, 10, 15 Median = 8hours and the inter-quartile range = 9 – 6 = 3 hours. The averages are similar but the measures of spread are significantly different since the extreme values of 2 and 15 are not included in the inter-quartile range.

  13. Box Plots Box and Whisker Diagrams. Box plots are useful for comparingtwo or more sets of data like that shown below for heights of boys and girls in a class. Anatomy of a Box and Whisker Diagram. Median Whisker Whisker Box Boys cm Girls 130 140 150 160 170 180 190 4 5 6 7 8 9 10 11 12 Lower Quartile Upper Quartile Lowest Value Highest Value

  14. Drawing a Box Plot. Example 1: Draw a Box plot for the data below 4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12 Q2 Q1 Q3 Upper Quartile = 9 Lower Quartile = 5½ Median = 8 4 5 6 7 8 9 10 11 12

  15. Drawing a Box Plot. Example 2: Draw a Box plot for the data below 3, 4, 4, 6, 8, 8, 8, 9, 10, 10, 15, Q2 Q3 Q1 Upper Quartile = 10 Lower Quartile = 4 Median = 8 12 13 3 4 5 6 7 8 9 10 11 14 15

  16. Drawing a Box Plot. Question: Stuart recorded the heights in cm of boys in his class as shown below. Draw a box plot for this data. Q2 Qu QL 137, 148, 155, 158, 165, 166, 166, 171, 171, 173, 175, 180, 184, 186, 186 Upper Quartile = 180 Lower Quartile = 158 Median = 171 130 140 150 160 170 180 cm 190

  17. Q2 Q1 Q3 Upper Quartile = 9 Lower Quartile = 5½ Median = 8 Finding the median, quartiles and inter-quartile range. Example 1: Find the median and quartiles for the data below. 12, 6, 4, 9, 8, 4, 9, 8, 5, 9, 8, 10 Order the data 4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12 Inter-Quartile Range = 9 - 5½ = 3½

  18. Q2 Q3 Q1 Upper Quartile = 10 Lower Quartile = 4 Median = 8 Finding the median, quartiles and inter-quartile range. Example 2: Find the median and quartiles for the data below. 6, 3, 9, 8, 4, 10, 8, 4, 15, 8, 10 Order the data 3, 4, 4, 6, 8, 8, 8, 9, 10, 10, 15, Inter-Quartile Range = 10 - 4 = 6

  19. Discuss the calculations below. Battery Life: The life of 12 batteries recorded in hours is: 2, 5, 6, 6, 7, 8, 8, 8, 9, 9, 10, 15 Mean = 93/12 = 7.75hours and the range = 15 – 2 = 13 hours. 2, 5, 6, 6, 7, 8, 8, 8, 9, 9, 10, 15 Median = 8hours and the inter-quartile range = 9 – 6 = 3 hours. The averages are similar but the measures of spread are significantly different since the extreme values of 2 and 15 are not included in the inter-quartile range.

  20. Box Plots Box and Whisker Diagrams. Box plots are useful for comparingtwo or more sets of data like that shown below for heights of boys and girls in a class. Anatomy of a Box and Whisker Diagram. Median Whisker Whisker Box Boys cm Girls 130 140 150 160 170 180 190 4 5 6 7 8 9 10 11 12 Lower Quartile Upper Quartile Lowest Value Highest Value

  21. Drawing a Box Plot. Example 1: Draw a Box plot for the data below 4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12 Q2 Q1 Q3 Upper Quartile = 9 Lower Quartile = 5½ Median = 8 4 5 6 7 8 9 10 11 12

  22. Drawing a Box Plot. Example 2: Draw a Box plot for the data below 3, 4, 4, 6, 8, 8, 8, 9, 10, 10, 15, Q2 Q3 Q1 Upper Quartile = 10 Lower Quartile = 4 Median = 8 12 13 3 4 5 6 7 8 9 10 11 14 15

  23. Drawing a Box Plot. Question: Stuart recorded the heights in cm of boys in his class as shown below. Draw a box plot for this data. Q2 Qu QL 137, 148, 155, 158, 165, 166, 166, 171, 171, 173, 175, 180, 184, 186, 186 Upper Quartile = 180 Lower Quartile = 158 Median = 171 130 140 150 160 170 180 cm 190

  24. Objective • Reviewing various graphing techniques • Histogram • Bar Graphs • Scatterplots • Box and whisker plots

  25. Histograms • Used to plot a single set of data. • Data needs to be quantitative data. • You graph them in terms of frequency. • Bars should be directly next to each other. • The bin length refers to how wide each frequency group is (it needs to be constant

  26. Histograms: Example • Bin length: 5 (ft.)

  27. Bar Graphs • Also used to graph a single set of data • Data needs to be categorical • Data still graphed via frequency • Bars don’t touch (label under each bar)

  28. Bar Graph: Example

  29. Scatterplots • Used to graph a double set of data - meaning that there is two sets of data (x and y). • Data needs to quantitative. • One set of data is graphed on the x axis, one on the y • (where the x and y values meet is your point) • A positive correlation has data generally goes up. • A negative correlation has data generally goes down. • No correlation means there is no relationship

  30. Scatterplot: Example

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