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Chapter Two

Chapter Two. Summarising numerical data: the median, range, interquartile range and box plots. The two most commonly used types of statistics are classified as: Measures of centre Measures of spread. Summary Statistics for Numerical Data.

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Chapter Two

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  1. Chapter Two Summarising numerical data: the median, range, interquartile range and box plots

  2. The two most commonly used types of statistics are classified as: Measures of centre Measures of spread Summary Statistics for Numerical Data

  3. The median is the middle value when the data is ordered. The median depends on position in the set of data and so is not distorted by extreme values and outliers. The MedianA measure of centre

  4. The Range is the difference between the maximum value and the minimum value. The Interquartile Range (IQR) is the spread of the middle 50% of the data. Range & Interquartile Range: Measures of Spread

  5. 2 9 1 8 3 5 3 8 1 Place numbers in ascending order 1 1 2 3 3 5 8 8 9 Median = 3 (5th score) Calculating the median

  6. 1 1 2 3 3 5 8 8 9 Calculating the Range Max = 9 Min = 1 Range = Max – Min Range = 9 – 1 Range = 8

  7. 1 1 2 3 3 5 8 8 9 Calculating the Quartiles Median (Q2) =3 Upper Quartile (Q3) Lower Quartile (Q1) Q1 = 1.5 Q3 = 8 IQR = Q3 – Q1 IQR = 8 – 1.5 IQR = 6.5

  8. 1 2 3 3 5 6 2 3 4 5 7 8 8 3 0 1 3 3 7 4 0 0 5 5 1 6 6 0 Stem and Leaf Plots There are 22 scores The median will be between the 11th and 12th score. Median = 29 Lower Quartile = 23 Upper Quartile = 40 IQR = 40 –23 IQR = 17 Exercise 2A Pages 39 – 40 Questions 1-7

  9. 1 1 2 3 3 5 8 8 9 Five number summary maximum median minimum 9 1 3 Upper Quartile Q3 Lower Quartile Q1 8 1.5 IQR = 6.5

  10. Min = 1 Q1 = 1.5 Median = 3 Q3 = 8 Max = 9 Five Number Summary

  11. A Box and Whisker Plot illustrates the 5 number summary. It is often used as a visual comparison of similar data sets. The statistics median, IQR and Range can be easily observed from a boxplot. Box and Whisker Plot

  12. Box and Whisker Plot The box represents the middle 50% of the scores ie the IQR Each whisker represents 25% of the scores

  13. Box and whisker plot Exercise 2B Page 44 Question 1 and 2

  14. Outliers are identified using the limits Q1 – 1.5*IQR and Q3 + 1.5*IQR Any data values outside these boundaries are marked with an asterix on the boxplot. Box Plot with Outliers

  15. 1 2 3 3 2 3 4 5 7 8 3 0 1 3 8 4 5 6 0 Boxplot with outliers Min = Q1 = Med = Q3 = Max = 12 18 27 IQR = 14 32 60 = -3 Q1-1.5*IQR = 18 – 1.5*14 Boxplot limits Q3+1.5*IQR = 32 + 1.5*14 = 53 60 will be an outlier

  16. Boxplot with outliers

  17. Calculator display Exercise 2B Questions 3 – 6 Using a calculator

  18. Relating the shape of a histogram to a box plot Symmetric

  19. Relating the shape of a histogram to a box plot

  20. Relating the shape of a histogram to a box plot

  21. Exercise 2C Page 47 All Questions

  22. Comparing Boxplots

  23. Exercise 2D Page 49 All Questions

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