1. 5,8,12,15,15,18,20,20,20,30,35,40,50 510 15 20 25 30 354045 50 Drawing a Dot plot

2. BOX PLOTS

3. MEDIAN UPPER QUARTILE LOWER QUARTILE LOWEST VALUE HIGHEST VALUE

4. 9 3616 151416 14

5. 9 14 15 16 36 LOWER QUARTILE MEDIAN UPPER QUARTILE 5 figure summary 1.Highest Value = 36 2.Lowest value = 9 3.Median = 15 4.Lower Quartile = 14 5.Upper Quartile = 16

6. 9 14 15 16 36 LOWER QUARTILE MEDIAN UPPER QUARTILE Inter quartile Range = Upper Quartile – Lower Quartile = 16 – 14 = 2 5 figure summary 1.Highest Value = 36 2.Lowest value = 9 3.Median = 15 4.Lower Quartile = 14 5.Upper Quartile = 16

7. WHY? The IQR measures the middle 50% of our data Extreme values are therefore eliminated

8. BOX PLOTS

9. MEDIAN UPPER QUARTILE LOWER QUARTILE LOWEST VALUE HIGHEST VALUE

10. Why a box plot? This shows the inter-quartile range in relation to the median They can be used to compare different sets of data The smaller the IQR is, the more consistent the data will be

11. These box plots show how 2 classes performed in a test. Compare the two box plots. 510 15 20 25 30 354045 50 A B

13. EXAMPLE 1 (An odd number of values) Andy records the length of time of his mobile phone calls over 1 week. All the times are in minutes: 5,8,12,15,16,16,18,20,21,25,30,35,36,40,50. Work out the median, the lower and upper quartiles from his data and draw a box plot.

14. 5,8,12,15,16,16,18,20,21,25,30,35,36,40,50 510 15 20 25 30 354045 50 IQR = 20 minutes LOWER QUARTILE UPPER QUARTILE

15. 8,12,15,16,16,18,20,21,25,30,35,36,40,50 The median of the lower half =LOWER QUARTILE. The median of the upper half =UPPER QUARTILE The median is 20.5 There are 7 numbers in each half EXAMPLE 2 (An even number of values)

16. 8,12,15,16,16,18,20,21,25,30,35,36,40,50 The median is 20.5 The median occurs between the 7 th & 8 th value The rule is (n+1)/2

17. FINDING OUTLIERS 510 15 20 25 30 354045 50 Work out 1.5 x IQR; 1.5 x 20 = 30 Outliers will be more than 30 above the UQ → 30 + 35 = 65 ie outliers are above 65

18. FINDING OUTLIERS 510 15 20 25 30 354045 50 Work out 1.5 x IQR; 1.5 x 20 = 30 Outliers will be less than the LQ - 30 → 15 – 30 = -15 ie outliers are below -15

19. A symmetrical distribution 510 15 20 25 30 354045 50 This shows that the data is evenly spread about the median

20. A positive skew 510 15 20 25 30 354045 50 This shows that more of the data has smaller values

21. A negative skew 510 15 20 25 30 354045 50 This shows that more of the data will have larger values

22. 5,8,12,15,15,18,20,20,20,30,35,40,50 510 15 20 25 30 354045 50 Drawing a Dot plot