Cumulative Frequency and Box Plots Cumulative Frequency Curves

Cumulative Frequency and Box Plots

Cumulative Frequency Curves • Cumulative Frequency = a running total of the data • Median = Half way up the Cumulative Frequency (Q 2) • Lower Quartile = ¼ way up Cumulative Freq (Q 1) • Upper Quartile = ¾ way up Cumulative Freq (Q 3) • Inter Quartile Range = Q 3 – Q 1 • 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 0<t≤ 5 10 5 < t ≤ 10 16 10 < t ≤ 15 30 15 < t ≤ 20 22 20 < t ≤ 25 2 Cumulative Frequency 10 26 56 78 80

80 Cum freq x 60 x x Median = Middle Value 40 QUARTILES • Lower Quartile = ¼ way • Upper Quartile = ¾ way x 20 x 5 8½ 10 12½ 15 20 Interquartile Range = 15½ - 8½ = 7 mins 25 t 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 (Q 1) – 3. The Median (Q 2) – 4. Upper Quartile (Q 3) – 5. 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

60 30 ½ 20 10 0 L 0 10 ¼ Q 3 = 38 40 ¾ Median = 27 50 Q 1 = 21 Cumulative Frequency Box Plot from Cumulative Frequency Curve 70 IQR = 38 – 21 = 17 mins H 10 20 30 40 50 60 70 Minutes Late Q 1 Q 2 Q 3 20 30 40 50 60

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