Cumulative Frequency Curves Cumulative frequency table Cumulative frequency diagrams are used to obtain an estimate of the median, and quartiles. from a set of grouped data. Constructing a cumulative frequency table is first step. Cumulative Frequency just means running total. < 60 5 50 - 60 < 50 8 40 - 50 < 40 12 30 - 40 < 30 22 20 - 30 < 20 10 - 20 < 10 0 - 10 Cumulative Frequency Upper Limit Frequency Minutes Late Example 1. During a 4 hour period at busy airport the number of late-arriving aircraft was recorded. 5 13 35 47 55 60

Cumulative frequency table 60 < 60 5 50 - 60 55 < 50 8 40 - 50 47 < 40 12 30 - 40 35 < 30 22 20 - 30 13 < 20 10 - 20 < 10 0 - 10 CF Upper Limit f Mins Late 10 20 30 40 50 70 Cumulative Frequency Minutes Late Plotting the curve ¾ UQ = 38 ½ IQR = 38 – 21 = 17 mins Median = 27 ¼ LQ = 21 Plot the end point of each interval against cumulative frequency, then join the points to make the curve. Get an estimate for the median. Find the lower quartile. Find the Upper Quartile. Find the Inter Quartile Range.(IQR = UQ - LQ)

Cumulative Frequency Curves Cumulative frequency diagrams are used to obtain an estimate of the median and quartiles from a set of grouped data. Constructing a cumulative frequency table is first step. Example 2. A P.E teacher records the distance jumped by each of 70 pupils. d  260 5 250  d  260 d  250 8 240  d  250 d  240 18 230  d  240 d  230 15 220  d  230 d  220 7 210  d  220 d  210 9 200  d  210 d  200 6 190  d  200 d  190 2 180  d  190 Cumulative Frequency Upper Limit No of pupils Distance (cm) Cumulative frequency table 2 8 17 24 39 57 65 70 Cumulative Frequency just means running total.

Cumulative Frequency Table 10 20 30 40 50 60 70 180 190 200 210 220 230 240 250 260 Cumulative Frequency Distance jumped (cm) 5 250  d  260 65 8 240  d  250 57 18 230  d  240 39 15 220  d  230 24 7 210  d  220 17 9 200  d  210 6 190  d  200 2 180  d  190 Number of pupils Plotting The Curve Cumulative Frequency Table ¾ UQ = 237 ½ IQR = 237 – 212 = 25 cm Median = 227 ¼ LQ= 212 Plot the end point of each interval against cumulative frequency, then join the points to make the curve. Find the Lower Quartile. Get an estimate for the median. Find the Upper Quartile. Find the Inter Quartile Range.(IQR = UQ - LQ)

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

Example 1 Cumulative Frequency Minutes Late 70 60 50 40 30 20 10 < 60 5 50 - 60 < 50 8 40 - 50 < 40 12 30 - 40 < 30 22 20 - 30 < 20 10 - 20 < 10 0 - 10 CF Upper Limit f Mins Late 10 20 30 40 50 60 70 Cumulative Frequency Minutes Late

Example 2 Cumulative Frequency Distance jumped (cm) 10 20 30 40 50 60 70 180 190 200 210 220 230 240 250 260 Cumulative Frequency Distance jumped (cm) 5 250  d  260 8 240  d  250 18 230  d  240 15 220  d  230 7 210  d  220 9 200  d  210 6 190  d  200 2 180  d  190 Number of pupils Example 2