Transcript 2.1 Discrete and Continuous Variables

2.1 Discrete and Continuous
Variables
2.1.1 Discrete Variable
2.1.2 Continuous Variable
2.1.1 Discrete Variable

These are the heights of 20 children in a school. The heights have
been measured correct to the nearest cm. For example
133
131
130
134
136
127
131
135
120
141
125
137
138 133
127 143
144 128
133 129
 . For example


144 cm ( correct to the nearest cm) could have arisen from any
the range 143.5cm  h < 144.5 cm.
value in
Other examples of continuous data are
 the speed of vehicles passing a particular point,
 the masses of cooking apples from a tree,
 the time taken by each of a class of children to perform a task.

**Continuous data cannot assume exact value, but can be given
only within a certain range or measured to a certain degree of
accuracy,**
2.1.2 Continuous Variable
 There are the marks obtained by 30 pupils in a
test:
63 5 9 0 1 8 5 6 7 4 4 3 1 0
2 2 7 10 9 7 5 4 6 6 2 1 0 8 8
 the number of cars passing a checkpoint in a
certain time,

the shoe sizes of children in a class,

the number of tomatoes on each of the plants
2.2 Frequency Tables
2.2.1 Frequency Tables for Discrete Data
2.2.2 Frequency Tables for Continuous Data

fi
ri 
Relative Frequency is ri
N , where ri is the
relative frequency for the class i
k


i
and N =
Percentage Frequency can be
i 1
obtained by multiplying the relative frequency by
100%.
f
2.2.1 Frequency Tables for
Discrete Data
No. of vehicles
passing per minute, x
Frequency
6 or below
15
7-8
14
9-10
15
11-12
12
13-14
11
15 or above
3
Total
% frequency
cumulative
% frequency
2.2.2 Frequency Tables for
Continuous Data
Weight
Class mark
frequency
50.5 – 55.5
53
1
55.5 – 60.5
58
4
60.5 – 65.5
63
15
65.5 – 70.5
68
18
70.5 – 75.5
73
9
75.5 – 80.5
78
3
Total
% frequency
cumulative
% frequency
2.3 Graphical Representation
2.3.1 Bar Charts
2.3.2 Histograms
2.3.3 Frequency Polygons and Frequency
Curves
2.3.4 Cumulative Frequency Polygons and
Curves
2.3.5 Stem-and-leaf Diagrams
2.3.6 Logarithmic graphs
2.3.1 Bar Charts
 The frequency distribution of a discrete
variable can be represented by a bar chart.
2.3.2 Histograms
 A continuous frequency distribution
CANNOT be represented by a bar chart. It is
most appropriately represented by a
histogram.
2.3.3 Frequency Polygons and
Frequency
Curves
 Frequency Polygons
 Frequency Curves
 Relative frequency polygons
 Relative frequency curves
2.3.4 Cumulative Frequency
Polygons and
Curves
Example


The heights of 30 broad bean plants were measured, correct to the
nearest cm, 6 weeks after planting. The frequency distribution is given
below.
Height (cm)
3-5
6-8
9-11
12-14
15-17
18-20
Frequency
1
2
11
10
5
1





Construct the cumulative frequency table.
Construct the cumulative frequency curve.
Estimate from the curve
the number of plants that were less than 10 cm tall;
the value of x, if 10% of the plants were of height x cm or more.
2.3.5 Stem-and-leaf Diagrams
 1) In the below diagram, stems are
hundreds
and leaves are units.
 The set of data in the diagram represents:
111,123,147,148,223,227,355,363,380,421,42
Stem (in 100)
Leaves (in 10)
3,500
1
11
23
2
23
27
3
55
63
4
21
23
5
00
47
80
48
 A householder’s weekly consumption of
electricity in kilowatt-hours during a period of
nine week in a winter were as follows:
338,354,341,353,351,341,353,346,341.
Please completed stem and leaf diagram .
Examination results of 11 students:
 English:23,39,40,45,51,55,61,64,65,72,78
 Chinese:37,41,44,48,58,61,63,69,75,83,89
One way to compare their performances in the two
subjects is by means of side by side stem-and-leaf
diagrams.
 The comparison can be made more
dramatic by back-to-back stem-and-leaf
diagram.
Answer
Stem (in 10) Leaves (in 1)
33
8
34
1
1
1
6
35
1
3
3
4
2.3.6 Logarithmic graphs