Starter

1
Starter

• List 5 types of continuous data
• List 3 types of discrete data
• Find the median of the following numbers
• 2, 3, 6, 5, 7, 7, 3, 1, 2, 5, 4
• Why is the value for the mean calculated from
  grouped frequency table an estimate?

2
Grouped Data
Time (minutes) Frequency
17-18 4
18-19 7
19-20 8
20-21 13
21-22 12
22-23 9
23-24 7
Total 60
3
Finding the Mean
Time (minutes) Frequency f
4
7
8
13
12
9
7
Total 60
Midpoint t
t x f
17 t lt 18
17.5
17.5 x 4 70
18 t lt 19
18.5
18.5 x 7 129.5
19.5
19.5 x 8 156
19 t lt 20
mean 1247
20 t lt 21
20.5
20.5 x 13 266.5
60
21.5 x 12 256
21 t lt 22
21.5
20.8 (3s.f.)
22.5
22 t lt 23
22.5 x 9 202.5
23 t lt 24
23.5
23.5 x 7 164.5
Total 1247
4
Continuous Data
Data that can take any value (within a
range) Examples time, weight, height, etc.
You can imagine the class boundaries as fences
between a continuous line of possible values
0
time (for example)
2
4
6
8
10
These classes would be written as 0 t lt 2 2
t lt 4 4 t lt 6 6 t lt 8 8 t lt 10

• Each class has
• An upper bound
• A lower bound
• A class width
• A midpoint

5
Discrete Data
Data that can only take certain values Examples
number of people, shoe size.
There are only certain values possible. Classes
are like a container that hold certain values
0
n, number of people
2
4
6
8
10
11
9
7
5
3
1
These classes would be written as 0 - 1 2 - 3 4
- 5 6 - 7 8 - 9 10 - 11

• Each class has
• An upper bound
• A lower bound
• A class width
• A midpoint

6
Cumulative Frequency
Time (minutes) Frequency f
4
7
8
13
12
9
7
Total 60
Time (minutes) Frequency f
4







17 t lt 18
17 t lt 18
18 t lt 19
17 t lt 19
11
19
19 t lt 20
17 t lt 20
32
20 t lt 21
17 t lt 21
21 t lt 22
17 t lt 22
44
53
22 t lt 23
17 t lt 23
60
23 t lt 24
17 t lt 24
7
Cumulative Frequency Curve
f
60
Line is a smooth curve NOT straight lines between
each point
Time (minutes) Frequency f
4






50
17 t lt 18
40
17 t lt 19
11
30
19
17 t lt 20
32
17 t lt 21
20
17 t lt 22
44
plot points at the upper limit of each class
53
10
17 t lt 23
60
17 t lt 24
t
17
18
19
20
21
22
23
24
8
The Median and the Quartiles
The median is the middle value. Another way of
thinking about it is to consider at what value
exactly half of the samples were smaller and half
were bigger. We also look at the quartiles The
lower quartile is the value at which 25 of the
samples are smaller and 75 are bigger. If we had
60 runners in a race, it would be the time the
15th runner finished, 25 were quicker, 75 were
slower. The upper quartile is the value at which
75 of the samples are smaller and 25 are
bigger. Again, for 60 runners, it would be the
time the 45th person finished. 75 were quicker,
25 were slower. The interquartile range
(IQR) upper quartile lower quartile Q3
Q1 The IQR gives a measure of the spread of the
data.
Q1 is the first quartile, or the lower
quartile Q2 is the second quartile, or the
median, m Q3 is the third quartile, or the upper
quartile
9
Finding the median
f
Median m or Q2 We find the value of t when f
30
60
50
Upper quartile Q3 We find the value of t when f
45
40
30
Lower quartile Q1 We find the value of t when f
15
20
10
t
17
18
19
20
21
22
23
24
Q1
Q2
Q3
10
Interquartile Range
The interquartile range (IQR) upper quartile
lower quartile Q3 Q1 The IQR gives a measure
of the spread of the data. The data between Q1
and Q3 is half of the samples. How packed
together are these results? The IQR gives us a
measure of this. If the IQR is small, the
cumulative frequency curve will be steeper in the
middle. This means that more samples are nearer
to the mean, If the IQR is large, the cumulative
frequency curve will not be so steep in the
middle. The samples are more spread out.
11
Page 320Exercise 117Questions 13, 14, 15 16
12
PRINTABLE SLIDES

• Slides after this point have no animation.

13
Cumulative Frequency
Time (minutes) Frequency f
4
7
8
13
12
9
7
Total 60
Time (minutes) Frequency f
4







17 t lt 18
17 t lt 18
18 t lt 19
17 t lt 19
11
19
19 t lt 20
17 t lt 20
32
20 t lt 21
17 t lt 21
21 t lt 22
17 t lt 22
44
53
22 t lt 23
17 t lt 23
60
23 t lt 24
17 t lt 24
14
Cumulative Frequency Curve
f
60
Line is a smooth curve NOT straight lines between
each point
Time (minutes) Frequency f
4






50
17 t lt 18
40
17 t lt 19
11
30
19
17 t lt 20
32
17 t lt 21
20
17 t lt 22
44
plot points at the upper limit of each class
53
10
17 t lt 23
60
17 t lt 24
t
17
18
19
20
21
22
23
24
15
The Median and the Quartiles
The median is the middle value. Another way of
thinking about it is to consider at what value
exactly half of the samples were smaller and half
were bigger. We also look at the quartiles The
lower quartile is the value at which 25 of the
samples are smaller and 75 are bigger. If we had
60 runners in a race, it would be the time the
15th runner finished, 25 were quicker, 75 were
slower. The upper quartile is the value at which
75 of the samples are smaller and 25 are
bigger. Again, for 60 runners, it would be the
time the 45th person finished. 75 were quicker,
25 were slower. The interquartile range
(IQR) upper quartile lower quartile Q3
Q1 The IQR gives a measure of the spread of the
data.
Q1 is the first quartile, or the lower
quartile Q2 is the second quartile, or the
median, m Q3 is the third quartile, or the upper
quartile
16
Finding the median
f
Median m or Q2 We find the value of t when f
30
60
50
Upper quartile Q3 We find the value of t when f
45
40
30
Lower quartile Q1 We find the value of t when f
15
20
10
t
17
18
19
20
21
22
23
24
Q1
Q2
Q3
17
Interquartile Range
The interquartile range (IQR) upper quartile
lower quartile Q3 Q1 The IQR gives a measure
of the spread of the data. The data between Q1
and Q3 is half of the samples. How packed
together are these results? The IQR gives us a
measure of this. If the IQR is small, the
cumulative frequency curve will be steeper in the
middle. This means that more samples are nearer
to the mean, If the IQR is large, the cumulative
frequency curve will not be so steep in the
middle. The samples are more spread out.