1. PowerPointmaths.com © 2004 all rights reserved
© Where quality comes first!
PowerPointmaths.com © 2004 all rights reserved

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 2 4 5 7 10 27
0 - 10
frequency
minutes 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
135 15
150 25
175 35
175 45
180 55
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 2 4 5 7 10 27
0 - 10
frequency
minutes late
Data is grouped into 6 class intervals of width 10.

4. The modal class is simply the class interval of highest frequency.
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 2 4 5 7 10 27
0 - 10
frequency
minutes late
The modal class is simply the class interval of highest frequency.
Modal class =

5. The 28th data value is in the 10 - 20 class
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. 2 4 5 7 10 27
0 - 10
frequency
minutes late
(55+1)/2
= 28
The 28th data value is in the class

6. 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 1 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.

7. Grouped Data Mean estimate = 1828/91 = 20.1 laps Example 2.
mp x f
midpoint(x) 1 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:
(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 6 8 72 13
195 18
360 23
391 28
700 33 66 38 38
Mean estimate = 1828/91 = 20.1 laps

8. Grouped Data Example 2. Modal Class 26 - 30
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. 1 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
Modal Class

9. Grouped Data Example 2. (91+1)/2 = 46 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
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
The 46th data value is in the 16 – 20 class 
(91+1)/2 = 46

10. Averages From Grouped Data
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 2 4 5 7 10 27
0 - 10
frequency
minutes 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. 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. 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 4 5 7 10 27
0 - 10
frequency
minutes Late

12. 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 2
31 – 35 25
26 – 30 17
21 – 25 20
16 – 20 15
11 – 15 9
6 – 10
1 - 5
frequency
number of laps