Transcript Further Mathematics Univariate data

Collecting Data
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Name
Number of Siblings
Preferred Football Team
Star Sign
Hand Span
Univariate Data
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Categorical: a category is recorded
when the data is collected. Examples of
categorical data include gender,
nationality, occupation.
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Numerical: when data is collected a
number is recorded.
Univariate Data
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There are two types of numerical data
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Discrete: the numbers recorded are distinct
values, often whole numbers and usually the data
comes from counting. Examples include number of
students in a class, pages in a book.
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Continuous: any number on a continuous line is
recorded; usually the data is produced by
measuring to any desired level of accuracy.
Examples include volume of water consumed, life
of a battery.
The age of my car is numerical data
TRUE
FALSE
The colour of my car is categorical data
TRUE
FALSE
The number of cars in the car park would be
considered numerical & continuous data.
TRUE
FALSE
If I rate my driving experience of some test cars
between one and ten, this is considered numerical
& discrete data.
TRUE
FALSE
Categorical data has a specific graduated order
TRUE
FALSE
Continuous numerical data can be measured
TRUE
FALSE
If 1 = satisfied, 2 = indifferent & 3 = dissatisfied, I
am collecting categorical data
TRUE
FALSE
I cannot get a mean if the data is categorical
TRUE
FALSE
Univariate Data
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Exercise 1A – 3 & 4
Univariate Data
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Summarising data
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Frequency tables: may be used with both
categorical and numerical data. Class
intervals are used to group continuous
numerical data or to group discrete data
where there is a large range of values.
Categorical Data
Favourite team
Frequency % Frequency
Collingwood
12
12/35 * 100 = 34%
Essendon
Bulldogs
Carlton
Total
5
15
3
35
14%
43%
9%
100%
Categorical Data
Bar Graph / Column Graph
Preferred Football Team
16
14
Frequency
12
10
8
6
4
2
0
Collingwood
Essendon
Bulldogs
Team
Carlton
Percentaged Segmented Bar
Chart
Percentaged Segmented Barchart of Favourite Teams
100%
Carlton
Percentage Frequency
90%
80%
Bulldogs
70%
60%
50%
40%
Essendon
30%
20%
Collingwood
10%
0%
Team
Numerical Data
Dot Plots
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Dots plots are used with discrete data
and small samples
1
2
3
4
5
Number of siblings
Numerical Data
Number of
Siblings
Frequency
0
2
Percentage
Frequency
2/25*100 = 8%
1
2
3
4
12
7
25
16%
48%
28%
100%
Numerical Data
Histogram
Numerical Data
Handspan
Frequency
Percentage Frequency
200 – 209
10
10/30 * 100 = 33%
210 – 219
220 – 229
230 – 239
15
3
2
30
50%
10%
7%
100%
Numerical data Histogram
Mode
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The mode is the most commonly
occurring category, value or interval.
Numerical Data
Stem and Leaf Plots
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Stem and Leaf Plots display the distribution of
numerical data (both discrete and
continuous) as well as the actual data values.
An ordered stem and leaf plot is obtained by
ordering the numbers in the leaf in ascending
order.
A stem and leaf plot should have at least 5
numbers in the stem
Numerical Data
Stem and Leaf Plots
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Stem
20
21
22
23
24
Leaf
12256
012
238
24
0
02
represents 240
Numerical Data
Stem and Leaf Plots
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Sometimes it may be necessary to split
the stems in order to obtain the
required number of stems.
Consider the data
12 4
6
8
10
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16
19
5
Numerical Data
Describing a distribution
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Shape
Generally one of three types
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Symmetric
Positively Skewed
Negatively Skewed
Numerical Data
Shape Symmetric
Symmetric (same shape either
side of the centre)
Numerical Data
Shape: Positively Skewed
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Positively skewed : tails off to the right
Numerical Data
Shape: Negatively Skewed
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Negatively skewed : tails off to the left
Centre
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The centre is the value which has the
same number of scores above as below.
Spread
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The maximum and minimum values
should be used to calculate the range.
Range = Maximum Value – Minimum Value
Outliers
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Outliers are extreme values well away
from the majority of the data
Describe this distribution
Questions from Chapter One
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Neat Theory book
Neat Practical book
Exercise 1B Page 7-8 Questions 2,4,6,8
Exercise 1C Pages 14-15 Questions 1-7
Exercise 1E Page 26 Question 1
Exercise 1D Pages 19-21 Questions 1 - 4
Exercise 1E Pages 26-28 Questions 2,3,4,6,7,8
Chapter One Review Pages 30 – 34