Cumulative Frequency and Box Plots Learning Objectives To

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Cumulative Frequency and Box Plots

Cumulative Frequency and Box Plots

Learning Objectives To be able to draw a cumulative frequency curve and use it

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

Does anybody remember how to draw a Cumulative Frequency Diagram?

Does anybody remember how to draw a Cumulative Frequency Diagram?

Cumulative Frequency Curves • Cumulative Frequency = a running total of the data •

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

Big Worked Example The table below shows the number of minutes students were late

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) Number of Students 0<t≤ 5 10 5 < t ≤ 10 16 10 < t ≤ 15 30 15 < t ≤ 20 22 20 < t ≤ 25 2 Cumulative Frequency

80 x x Cum freq 60 x Median = Middle Value 40 QUARTILES •

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 15 20 = 15½ - 8½ = 7 mins 25 t mins

Does anybody have any idea what a Box Plot is?

Does anybody have any idea what a Box Plot is?

Box Plots • Box Plots (Box and Whisker Diagram) are another way of displaying

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 (Q 1) The Median (Q 2) Upper Quartile (Q 3) Maximum Value They are drawn in the following way: 1 2 3 4 • BOX = The location of the middle 50% of the data • WHISKERS = How the data is spread overall 5

Box Plot from Cumulative Frequency Curve 70 50 ¾ 40 10 0 ¼ 10

Box Plot from Cumulative Frequency Curve 70 50 ¾ 40 10 0 ¼ 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

Box Plot Lowest value Lower Quartile 0 Highest value Median 5 10 Upper Quartile

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

Work • Ex 7: 1 – Page 62 – Questions 5 and 6

Work • Ex 7: 1 – Page 62 – Questions 5 and 6