Cumulative Frequency Curves Cumulative frequency diagrams are used

Cumulative Frequency Curves Cumulative frequency diagrams are used

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 1. During a 4 hour period at busy Cumulative frequency airport the table number of lateMinutes Frequency Upper Cumulative Limit Frequency arriving aircraft Late was recorded. 0 - 10 5 < 10 5 10 - 20 8 < 20 13 20 - 30 22 < 30 35 30 - 40 12 < 40 47 40 - 50 8 < 50 55 50 - 60 5 < 60 60 Cumulative Frequency just means running total. Plotting the curve Cumulative frequency table 60 50 40 10 0

10 20 UQ = 38 20 IQR = 38 21 = 17 mins Median = 27 30 LQ = 21 Cumulative Frequency 70 30 40 50 60 Minutes Late Get an estimate for the median. Find the Upper 70 Mins Late f Upper Limit CF 0 - 10 5 < 10 5 10 - 20 8 < 20 13 20 - 30 22 < 30 35 30 - 40 12 < 40 47 40 - 50 8 < 50

55 50 - 60 5 < 60 60 Plot the end point of each interval against cumulative frequency, then join the points to make the curve. Find the lower 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. Cumulative frequency table Distance (cm) No of pupils Upper Limit Cumulative Frequency 180 d 190 2 d 190 190 d 200 6 d 200 2 8 200 d 210 9 d 210 17 210 d 220 7 d 220 24 220 d 230 15 d 230

39 230 d 240 18 d 240 57 240 d 250 8 d 250 65 250 d 260 5 d 260 70 Cumulative Frequency just means Plotting The Curve 60 Cumulative Frequency Table 50 20 10 0 IQR = 237 212 = 25 cm UQ = 237 30 Median = 227 40 LQ= 212 Cumulative Frequency 70 180 190 200 210 220 230 240 250 260 Distance jumped (cm) Number of pupils Cumulative Frequency 180 d 190 2 2 190 d 200

6 8 200 d 210 9 17 210 d 220 7 24 220 d 230 15 39 230 d 240 18 57 240 d 250 8 65 250 d 260 5 70 Plot the end point of each interval against cumulative frequency, then join the points to make the curve. Distance jumped (cm) Get an estimate for the median. Find the Upper Find the Lower Quartile. Find the Inter Quartile Range.(IQR = UQ - LQ) Box Plot from Cumulative Frequency Curve 60 50 40 10 0 10 20 UQ = 38 20 IQR = 38 21 = 17 mins Median = 27 30

LQ = 21 Cumulative Frequency 70 30 40 50 60 70 Minutes Late 0 10 20 30 40 50 60 Example 1 Cumulative Frequency 70 60 50 Mins Late f Upper Limit 40 0 - 10 5 < 10 10 - 20 8 < 20 20 - 30 22 < 30 30 - 40 12 < 40 40 - 50 8 < 50 50 - 60

5 < 60 30 20 10 0 10 20 30 40 50 60 Minutes Late 70 CF Example 2 Cumulative Frequency 70 60 50 40 30 20 10 0 180 190 200 210 220 230 240 250 260 Distance jumped (cm) Distance jumped (cm) Number of pupils 180 d 190 2 190 d 200 6 200 d 210 9 210 d 220 7 220 d 230 15 230 d 240 18 240 d 250 8 250 d 260 5 Cumulative Frequency

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