Alternate methods of analyising the data have to be employed. Grouped Data 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.

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.

Data is grouped into 6 class intervals of width 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. 2 50 - 60 4 40 - 50 5 30 - 40 7 20 - 30 10 10 - 20 27 0 - 10 frequency minutes late Data is grouped into 6 class intervals of width 10.

Mean estimate = 925/55 = 16.8 minutes 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. midpoint(x) fx 2 50 - 60 4 40 - 50 5 30 - 40 7 20 - 30 10 10 - 20 27 0 - 10 frequency minutes Late 5 135 15 150 25 175 35 175 45 180 55 110 Mean estimate = 925/55 = 16.8 minutes

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 calculate an estimate for the mean number of laps. 1 36 - 40 2 31 – 35 25 26 – 30 17 21 – 25 20 16 – 20 15 11 – 15 9 6 – 10 1 - 5 frequency (x) number of laps Data is grouped into 8 class intervals of width 4.

Mean estimate = 1828/91 = 20.1 laps Example 2. mp x f midpoint(x) 1 36 - 40 2 31 – 35 25 26 – 30 17 21 – 25 20 16 – 20 15 11 – 15 9 6 – 10 1 - 5 frequency 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 calculate an estimate for the mean number of laps. 3 6 8 72 13 195 18 360 23 391 28 700 33 66 38 38 Mean estimate = 1828/91 = 20.1 laps

Grouped Data Example 1. mp x f 2 50 - 60 4 40 - 50 5 30 - 40 7 20 - 30 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. midpoint(x) mp x f 2 50 - 60 4 40 - 50 5 30 - 40 7 20 - 30 10 10 - 20 27 0 - 10 frequency minutes Late

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. mp x f midpoint(x) 1 36 - 40 2 31 – 35 25 26 – 30 17 21 – 25 20 16 – 20 15 11 – 15 9 6 – 10 1 - 5 frequency number of laps