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 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 ≤ < t ≤ < t ≤ < t ≤ < t ≤ 25 2

t mins Cum freq x x x x x Median = Middle Value QUARTILES Lower Quartile = ¼ way Upper Quartile = ¾ way Interquartile Range 8½ 15½12½ = 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 (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

Box Plot from Cumulative Frequency Curve

Box Plot t mins 0 Lowest value Upper Quartile Highest value Lower Quartile Median

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