1. Discrete vs continuous
Count it or measure it?

2. Discrete
Continuous
You can count it.
The units of measurement cannot be split up.
E.g shoe size- you cannot have a size 5.2.
If you were to put it on a number scale, only certain numbers have a meaning.
You can measure it.
The whole units can be split up.
You can put it on a number scale.
Each value on the scale has a meaning e.g. 1.05kg

3. How many cows are there in that field?
Discrete
Continuous

4. How fast can your car go?
Discrete
Continuous

5. How much water is there in this bottle?
Discrete
Continuous

6. How many CDs do you own?
Discrete
Continuous

7. What is your shoe size?
Discrete
Continuous

8. How much does a whale weigh?
Discrete
Continuous

9. How much does a Mars Bar cost?
Discrete
Continuous

10. What is the temperature of this fire?
Discrete
Continuous

11. How long does the bus to Birchington take?
Discrete
Continuous

12. Discrete Qualitative Continuous
What is the breed of that dog?
Discrete
Qualitative
Continuous

13. Types of Average- Silent Starter – Write down accurate definitions of Mean, Mode, Median and Range
Mean - Add up the numbers and divide by how many there are
Mode - the value that occurs most often
Median - the middle value (you must put them in order first)
Range - the difference between the largest and smallest values

14. 6 6 6 8 4
WATCH CAREFULLY AND WRITE DOWN THE NUMBERS THAT APPEAR AND CALCUATE THE MMMR

15. 3 5 2 6 4 7 1

16. What is your method for finding the median?
Calculate the MMMR of the following data:
3,5,6,5,4,3,3,5,6,2,4,3,1,2,1,3,4,5,5,1,1,5,6,3,4,2,1,2,1,3,4,5,6,4,3,1,4,2,6,6
1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6
Mean = 140/40 = 3.5
Median = 4
Mode = 3
Range = 6-1= 5 2

17. Here is some data on class sizes in a school.
Frequency Tables
It is often convenient to record data in a frequency table. This is particularly useful when there is a large amount of data. The mean, mode, median and range can be calculated directly from the table.
Here is some data on class sizes in a school.
27, 27, 28, 28, 28, 28, 29, 29, 29, 30, 30, 30, 30, 30, 31, 31, 32
Data placed in a frequency table
Class Size 27 28 29 30 31 32 f 2 4 3 5 1

18. Objective (L7)
Calculate the Mode, Median, Mean and Range of grouped data.

19. Or if entered directly into a calculator.
What does the symbol for ‘the sum of’ look like?
Original data in list form:
27, 27, 28, 28, 28, 28, 29, 29, 29, 30, 30, 30, 30, 30, 31, 31, 32
Frequency Tables
Calculating the mean from the frequency table.
Class Size x 27 28 29 30 31 32 f 2 4 3 5 1 fx 54
112 87
150 62 32
Or if entered directly into a calculator.
(2 x x x x x x 32) 17
Mean =
= 497/17 = 29.2

20. Original data in list form:
27, 27, 28, 28, 28, 28, 29, 29, 29, 30, 30, 30, 30, 30, 31, 31, 32
Frequency Tables
Finding the mode, median and range from the frequency table.
Class Size 27 28 29 30 31 32 f 2 4 3 5 1
Median = 29 (The middle data value) [(17 + 1)/2 = 9th data value.]
Mode = 30 (Highest frequency)
Range = 32 – 27 = 5

21. 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
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

22. 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.

23. 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 =

24. 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

25. 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.

26. 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

27. 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

28. 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

29. Your Turn!

30. 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

31. 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

32. 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