Cumulative Frequency and Box Plots

Cumulative Frequency Curves Cumulative Frequency = a running total of the data Median = Half way up the Cumulative Frequency (Q2) Lower Quartile = ¼ way up Cumulative Freq (Q1) Upper Quartile = ¾ way up Cumulative Freq (Q3) Inter Quartile Range = Q3 – Q1 Semi Inter Quartile Range =

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 26 10 < t ≤ 15 30 56 15 < t ≤ 20 22 78 20 < t ≤ 25 2 80

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

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 ¾ ½ Median = 27 ¼ Q1 = 21 Q3 = 38 IQR = 38 – 21 = 17 mins H L 10 20 30 40 50 60 Q1 Q2 Q3

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