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Topic: Data Handling

AGREE LEARNING OBJECTIVES. Topic: Data Handling. LO: To be able to understand and produce box plots. PREPARE FOR LEARNING. STARTER. Calculate the median of these numbers: 5, 7, 3, 6, 10, 4, 8, 7, 7 3, 4, 5, 6, 7 , 7, 7, 8, 10 11, 8, 9, 10, 3, 6, 8, 10 3, 6, 8, 8, 9, 10, 10, 11.

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Topic: Data Handling

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  1. AGREE LEARNING OBJECTIVES Topic: Data Handling LO:To be able to understand and produce box plots. PREPARE FOR LEARNING STARTER Calculate the median of these numbers: 5, 7, 3, 6, 10, 4, 8, 7, 7 3, 4, 5, 6, 7, 7, 7, 8, 10 11, 8, 9, 10, 3, 6, 8, 10 3, 6, 8, 8, 9, 10, 10, 11

  2. Box plots

  3. PRESENT NEW INFO

  4. CONSTRUCT MEANING Quartiles • The quartiles split the data into quarters. • The lower quartile is a ¼ of the way into the data • The upper quartile is ¾ of the way into the data • The median is (i.e. ½) of the way into the data

  5. CONSTRUCT MEANING Quartiles • Here are the maths test results of 23 male students: 3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10 • Lower Quartile: = = = 6th = 4 • Median: = = = 12th = 7 • Upper Quartile: 3 x LQ = 18th = 9

  6. CONSTRUCT MEANING Quartiles • Below are the ages of 15 members of a golf club. Calculate the median and quartiles for the data. • Lower Quartile: = = = 4th = 24 • Median: = = = 8th= 33 • Upper Quartile: 3 x LQ = 12th= 57 20, 20, 21, 24, 27, 29, 33, 33, 36, 39, 50, 57, 60, 65, 65

  7. CONSTRUCT MEANING Quartiles • Quartiles are more useful when comparing two sets of data. • Here are the ages of another golf club. Calculate the median and quartiles and compare the ages of the members of the two golf clubs • Lower Quartile: = = = 4.5th = 27 • Median: = = = 9th= 47 • Upper Quartile: 3 x LQ = 13.5th= 54 18, 23, 25, 27, 27, 37, 38, 45, 47, 49, 49, 50, 50, 58, 61, 66, 69

  8. DEMONSTATE UNDERSTANDING Quartiles • Which golf club has more younger members? • Which golf club has more older members? • What can you say about the age profile of each golf club in general?

  9. CONSTRUCT MEANING Quartiles • The Interquartile Range(IQR) is the upper quartile – the lower quartile • It tells us how spread out the middle 50% of the data is • Smaller IQR means more consistency and vice-versa

  10. CONSTRUCT MEANING Quartiles “Members of golf club B are more similar in age than in golf club A”

  11. CONSTRUCT MEANING Box Plots • A box plot is a way of illustrating key information about a set of data • They are also very useful for comparing the distribution of two sets of data (e.g. boys vs girls)

  12. CONSTRUCT MEANING Box Plots • To draw a box plot, you need FIVE pieces of information: • The minimum value • The lower quartile • The median • The upper quartile • The maximum value

  13. CONSTRUCT MEANING Box Plots

  14. The Interquartile Range (IQR) is the UQ – LQ. It illustrates the spread of the middle 50% of the data. The larger the IQR, the more spread out, and less consistent the data. • Minimum Value: 3 • Lower Quartile: 4 • Median: 7 • Upper Quartile: 9 • Maximum Value: 10 • Interquartile Range: 5 0 10 8 4 7 2 5 1 3 6 9 Maths Test Scores

  15. The box plot below shows the data for 23 female students. • Girls median higher so on average, girls scored higher • IQR lower so girls results were more consistent • Girls minimum value was higher so boys scored the lowest GIRLS 0 10 8 4 7 2 5 1 3 6 9 BOYS 0 10 8 4 7 2 5 1 3 6 9 Maths Test Scores

  16. DEMONSTATE UNDERSTANDING Box Plots Draw box plots to represent the age of members of the two golf clubs

  17. REVIEW Box Plots • Below are the midday temperatures for Ringwood over the past 11 days (in oC). 20, 22, 16, 17, 16, 18, 20, 18, 16, 21, 18 • Below are the midday temperatures for Glasgow over the past 11 days (in oC). 17, 20, 20, 17, 16, 14, 13, 19, 21, 17, 18 • Draw box plots for the data and write some comments on what they tell you about the temperatures in Ringwood and Glasgow over the past 11 days.

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