2.1 Discrete and Continuous Variables

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2.1 Discrete and Continuous Variables

• 2.1.1 Discrete Variable
• 2.1.2 Continuous Variable

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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
• . For example
• 144 cm ( correct to the nearest cm) could have
  arisen from any value in the range 143.5cm ? h lt
  144.5 cm.
• 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,

133 136 120 138 133 131 127 141 127 143 130 131 125 144 128 134 135 137 133 129
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2.1.2 Continuous Variable

• There are the marks obtained by 30 pupils in a
  test
• 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
  in a greenhouse.

6 3 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
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2.2 Frequency Tables

• 2.2.1 Frequency Tables for Discrete Data
• 2.2.2 Frequency Tables for Continuous Data
• Relative Frequency is , where
  ri is the relative frequency for the class i
• and N Percentage Frequency can be
  obtained by multiplying the relative frequency by
  100.

ri
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2.2.1 Frequency Tables for Discrete Data
No. of vehicles passing per minute, x Frequency frequency cumulative frequency
6 or below 15
7-8 14
9-10 15
11-12 12
13-14 11
15 or above 3
Total
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2.2.2 Frequency Tables for Continuous Data
Weight Class mark frequency frequency cumulative 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
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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

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2.3.1 Bar Charts

• The frequency distribution of a discrete variable
  can be represented by a bar chart.

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2.3.2 Histograms

• A continuous frequency distribution CANNOT be
  represented by a bar chart. It is most
  appropriately represented by a histogram.

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2.3.3 Frequency Polygons and Frequency Curves

• Frequency Polygons
• Frequency Curves
• Relative frequency polygons
• Relative frequency curves

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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.
• 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.

Height (cm) 3-5 6-8 9-11 12-14 15-17 18-20
Frequency 1 2 11 10 5 1
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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
• 111,123,147,148,223,227,355,363,380,421,423,500

Stem (in 100) Leaves (in 10)
1 11 23 47 48
2 23 27
3 55 63 80
4 21 23
5 00
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• A householders 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 .

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• Examination results of 11 students
• English23,39,40,45,51,55,61,64,65,72,78
• Chinese37,41,44,48,58,61,63,69,75,83,89
• One way to compare their performances in the two
  subjects is by means of side by side
  stem-and-leaf diagrams.

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• The comparison can be made more dramatic by
  back-to-back stem-and-leaf diagram.

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Answer
Stem (in 10) Leaves (in 1)
33 8
34 1 1 1 6
35 1 3 3 4
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2.3.6 Logarithmic graphs