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Cumulative freqeuncy and_box_plots

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Cumulative freqeuncy and_box_plots

1. 1. Cumulative Frequency and Box Plots
2. 2. Learning Objectives • To be able to draw a cumulative frequency curve and use it to estimate the median and interquartile range and draw a box plot
3. 3. Does anybody remember how to draw a Cumulative Frequency Diagram?
4. 4. Cumulative Frequency Curves • Cumulative Frequency = a running total of the data • Median = Half way up the Cumulative Frequency • Lower Quartile (LQ) = ¼ way up Cum Freq • Upper Quartile (UQ) = ¾ way up Cum Freq • Inter Quartile Range = UQ - LQ
5. 5. Big Worked Example The table below shows the number of minutes students were late for their fun algebra lesson. (a) Draw a Cumulative Frequency Diagram of the data (b) Use it to find the Median, Lower Quartile, Upper Quartile, and Inter Quartile Range (c) Draw a Box-Plot assuming a minimum time of o minutes and a maximum of 25 minutes Time t (mins) 0<t≤5 5 < t ≤ 10 10 < t ≤ 15 Number of Students 10 16 30 15 < t ≤ 20 22 20 < t ≤ 25 2 Cumulative Frequency
6. 6. 80 x x Cum freq 60 x Median = Middle Value 40 QUARTILES •Lower Quartile = ¼ way •Upper Quartile = ¾ way x 20 x 5 8½ 10 Interquartile Range 12½ 15½ 15 20 = 15½ - 8½ = 7 mins 25 t mins
7. 7. Does anybody have any idea what a Box Plot is?
8. 8. Box Plots • Box Plots (Box and Whisker Diagram) are another way of displaying data for comparison • To draw a Box Plot we need FIVE pieces of information: • – – – – – 1. 2. 3. 4. 5. The Minimum Value Lower Quartile (Q1) The Median (Q2) Upper Quartile (Q3) Maximum Value They are drawn in the following way: 1 2 3 4 5
9. 9. Box Plot from Cumulative Frequency Curve 70 50 ¾ 40 ¼ 10 0 10 20 30 UQ = 38 20 IQR = 38 – 21 = 17 mins Median = 27 30 ½ LQ = 21 Cumulative Frequency 60 40 50 60 70 Minutes Late 0 10 20 30 40 50 60
10. 10. Box Plot Lowest value Lower Quartile 0 Highest value Median 5 10 Upper Quartile 15 20 25 t mins
11. 11. Work • Ex 7:1 – Page 62 – Questions 5 and 6