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. < < < < < < Cumulative Frequency Upper Limit FrequencyMinutes Late Example 1. During a 4 hour period at busy airport the number of late- arriving aircraft was recorded.
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 table 60< < < < < < CF Upper Limit f Mins Late Cumulative Frequency Minutes Late Plotting the curve Median = 27 LQ = 21 UQ = 38 IQR = 38 – 21 = 17 mins ½ ¼ ¾
Example 2. A P.E teacher records the distance jumped by each of 70 pupils. d d 260 d d 250 d d 240 d d 230 d d 220 d d 210 d d 200 d d 190 Cumulative Frequency Upper Limit N o of pupils Distance (cm) Cumulative frequency table 70 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 Cumulative Frequency Curves
Cumulative Frequency Distance jumped (cm) d d d d d d d d 190 Cumulative Frequency Number of pupils Distance jumped (cm) Plotting The Curve Cumulative Frequency Table Plot the end point of each interval against cumulative frequency, then join the points to make the curve. Get an estimate for the median. Median = 227 Find the Lower Quartile. Find the Upper Quartile. LQ= 212 UQ = 237 Find the Inter Quartile Range.(IQR = UQ - LQ) IQR = 237 – 212 = 25 cm ½ ¼ ¾
Box Plot from Cumulative Frequency Curve
Example 1
Cumulative Frequency Distance jumped (cm) d d d d d d d d 190 Cumulative Frequency Number of pupils Distance jumped (cm) Example 2