Cumulative Frequency Diagrams & Box Plots

1. Cumulative Frequency Diagrams & Box Plots OCR Stage 8

2. Cumulative Frequency 10 26 56 78 80

3. x 80 x Cum freq Interquartile Range = 15½ - 8½ = 7 mins 60 x Median = Middle Value 40 • QUARTILES • Lower Quartile = ¼ way • Upper Quartile = ¾ way x 20 x 8½ 12½ 15½ 5 10 15 20 25 t mins

4. Lowest value Highest value Median Lower Quartile Upper Quartile 0 5 10 15 20 25 t mins Box Plot

5. Cum freq Comparing 2 sets of data Median = 62kg Upper Quartile = 70kg Lower Quartile = 52kg Interquartile range = 70 – 52 = 18kg

6. Cum freq Comparing 2 sets of data Median = 78kg Upper Quartile = 89kg Lower Quartile = 66kg Interquartile range = 89 – 66 = 23kg

7. Median = 62kg Upper Quartile = 70kg Median = 78kg Lower Quartile = 52kg Highest = 96 Lowest = 34 Upper Quartile = 89kg Lower Quartile = 66kg Highest = 112 Lowest = 40 20 40 60 80 100 120 m kg 18 23 Box Plots GIRLS BOYS IQRs MEDIANS 78 and 62

8. Comparison statements • Boys have a larger MEDIAN so • on average, they are heavier than girls • the average boy is 16kg heavier than the average girl • Boys have larger Interquartile Range so • boys’ weights vary more than girls’ weights • Why do we NOT use the Range? • One extreme value can distort the comparison