Learning Objectives:
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
Slide 3:
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:
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 Cumulative Frequency 0 < t ≤ 5 10 5 < t ≤ 10 16 10 < t ≤ 15 30 15 < t ≤ 20 22 20 < t ≤ 25 2
Slide 5:
5 10 15 20 25 t mins Cum freq 20 40 60 80 x x x x x Median = Middle Value QUARTILES Lower Quartile = ¼ way Upper Quartile = ¾ way Interquartile Range 8½ 15½ 12½ = 15½ - 8½ = 7 mins
Slide 6:
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 (Q 1 ) 3. The Median (Q 2 ) 4. Upper Quartile (Q 3 ) 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
Do you have any idea what a Box Plot is?:
Do you have any idea what a Box Plot is?
Slide 8:
10 20 30 40 50 60 70 0 Cumulative Frequency 10 20 30 40 50 60 70 Minutes Late Median = 27 LQ = 21 UQ = 38 IQR = 38 – 21 = 17 mins ½ ¼ ¾ 0 10 20 30 40 50 60 Box Plot from Cumulative Frequency Curve
Box Plot:
Box Plot 5 10 15 20 25 t mins 0 Lowest value Upper Quartile Highest value Lower Quartile Median