Cumulative Frequency and Box Plots

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?

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 0 < t ≤ 5 5 < t ≤ 10 10 < t ≤ 15 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 Cumulative Frequency 0 < t ≤ 5 10 5 < t ≤ 10 16 10 < t ≤ 15 30 15 < t ≤ 20 22 20 < t ≤ 25 2

80 x x Cum freq 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 Interquartile Range = 15½ - 8½ = 7 mins

Does anybody have any idea what a Box Plot is?

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. The Minimum Value 2. Lower Quartile (Q1) 3. The Median (Q2) 4. Upper Quartile (Q3) 5. Maximum Value They are drawn in the following way: BOX = The location of the middle 50% of the data WHISKERS = How the data is spread overall 3 4 1 2 5

Box Plot from Cumulative Frequency Curve 10 20 30 40 50 60 70 Cumulative Frequency Minutes Late Median = 27 LQ = 21 UQ = 38 IQR = 38 – 21 = 17 mins ½ ¼ ¾ 10 20 30 40 50 60

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

Work Ex 7:1 Page 62 Questions 5 and 6