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2. Example 1. During 3 hours at Heathrow airport 55 aircraft arrived late. The number of minutes they were late is shown in the grouped frequency table below. Grouped Data midpoint(x) mp x f 250 - 60 440 - 50 530 - 40 720 - 30 1010 - 20 270 - 10 frequencyminutes Late Estimating the Mean: An estimate for the mean can be obtained by assuming that each of the raw data values takes the midpoint value of the interval in which it has been placed. 5 15 25 35 45 55 135 150 175 180 110 Mean estimate = 925/55 = 16.8 minutes

3. Large quantities of data can be much more easily viewed and managed if placed in groups in a frequency table. Grouped data does not enable exact values for the mean, median and mode to be calculated. Alternate methods of analyising the data have to be employed. Example 1. During 3 hours at Heathrow airport 55 aircraft arrived late. The number of minutes they were late is shown in the grouped frequency table below. Grouped Data 250 - 60 440 - 50 530 - 40 720 - 30 1010 - 20 270 - 10 frequencyminutes late Data is grouped into 6 class intervals of width 10.

4. Example 1. During 3 hours at Heathrow airport 55 aircraft arrived late. The number of minutes they were late is shown in the grouped frequency table below. Grouped Data The Modal Class 250 - 60 440 - 50 530 - 40 720 - 30 1010 - 20 270 - 10 frequencyminutes late The modal class is simply the class interval of highest frequency. Modal class = 0 - 10

5. ( 55+1)/2 = 28 Example 1. During 3 hours at Heathrow airport 55 aircraft arrived late. The number of minutes they were late is shown in the grouped frequency table below. Grouped Data The Median Class Interval The Median Class Interval is the class interval containing the median. 250 - 60 440 - 50 530 - 40 720 - 30 1010 - 20 270 - 10 frequencyminutes late The 28 th data value is in the 10 - 20 class

6. Data is grouped into 8 class intervals of width 4. Example 2. A group of University students took part in a sponsored race. The number of laps completed is given in the table below. Use the information to: (a) Calculate an estimate for the mean number of laps. (b) Determine the modal class. (c) Determine the class interval containing the median. Grouped Data 136 - 40 231 – 35 2526 – 30 1721 – 25 2016 – 20 1511 – 15 96 – 10 21 - 5 frequency (x)number of laps

7. mp x f midpoint(x) 136 - 40 231 – 35 2526 – 30 1721 – 25 2016 – 20 1511 – 15 96 – 10 21 - 5 frequencynumber of laps Example 2. A group of University students took part in a sponsored race. The number of laps completed is given in the table below. Use the information to: (a) Calculate an estimate for the mean number of laps. (b) Determine the modal class. (c) Determine the class interval containing the median. Grouped Data 3 8 13 18 23 28 33 38 6 72 195 360 391 700 66 38 Mean estimate = 1828/91 = 20.1 laps

8. Modal Class 26 - 30 Grouped Data Example 2. A group of University students took part in a sponsored race. The number of laps completed is given in the table below. Use the information to: (a) Calculate an estimate for the mean number of laps. (b) Determine the modal class. (c) Determine the class interval containing the median. 136 - 40 231 – 35 2526 – 30 1721 – 25 2016 – 20 1511 – 15 96 – 10 21 - 5 frequency (x)number of laps

9. 136 - 40 231 – 35 2526 – 30 1721 – 25 2016 – 20 1511 – 15 96 – 10 21 - 5 frequency (x)number of laps Example 2. A group of University students took part in a sponsored race. The number of laps completed is given in the table below. Use the information to: (a) Calculate an estimate for the mean number of laps. (b) Determine the modal class. (c) Determine the class interval containing the median. Grouped Data (91+1)/2 = 46 The 46 th data value is in the 16 – 20 class

10. Example 1. During 3 hours at Heathrow airport 55 aircraft arrived late. The number of minutes they were late is shown in the grouped frequency table below. Averages From Grouped Data midpoint(x) mp x f 250 - 60 440 - 50 530 - 40 720 - 30 1010 - 20 270 - 10 frequencyminutes Late Estimating the Mean: An estimate for the mean can be obtained by assuming that each of the raw data values takes the midpoint value of the interval in which it has been placed. 5 15 25 35 45 55 135 150 175 180 110 Mean estimate = 925/55 = 16.8 minutes Modal Class (55 +1 )/2 = 28 Median Class Interval

11. Example 1. During 3 hours at Heathrow airport 55 aircraft arrived late. The number of minutes they were late is shown in the grouped frequency table below. Grouped Data midpoint(x) mp x f 250 - 60 440 - 50 530 - 40 720 - 30 1010 - 20 270 - 10 frequencyminutes Late

12. mp x f midpoint(x) 136 - 40 231 – 35 2526 – 30 1721 – 25 2016 – 20 1511 – 15 96 – 10 21 - 5 frequencynumber of laps Example 2. A group of University students took part in a sponsored race. The number of laps completed is given in the table below. Use the information to: (a) Calculate an estimate for the mean number of laps. (b) Determine the modal class. (c) Determine the class interval containing the median. Grouped Data