Further Maths
Univariate Data
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Univariate meaning: One variable. One
quantity that changes. For example,
number of cars sold by a car salesman
Type of data: Numerical and Categorical
data.
Interpreting the data: Discrete and
continuous
Stem Plots
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One way of displaying data-how the data
is distributed.
Use this method if there are 50 (or less)
observations
Consist of two parts - a stem and a leaf, is
always the last digit.
Important!!!! Must always arrange the
data in ascending first (not necessarily if
using the graphic calculator)
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The stem may be broken into halves or
fifths if the data are bunched up closely.
The stem plot need to include a key
(similarly like a legend)
Frequency histograms, dot plots
and bar charts
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Other alternatives to display data, but
larger data sets (50 or over observations)
Frequency histograms and bar charts are
like column graphs, very similar except
that one is separated by a small equally
space.
Note: This course relies reasonably on the
use of the graphic calculator – LEARN
HOW TO USE IT!!!!
Segmented bar charts
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A single bar to represent all the data being
studied.
The information is presented as
percentages and so the total bar length
represents 100% of the data.
Describing the shape of stem plots
and histograms
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Symmetric distributions
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Skewed distributions
Distribution
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The spread of the data
 Symmetric distribution (single peak and the data trial
off on both sides of this peak in roughly the same
fashion)
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Negatively Skewed
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The data peak to the right and trial off to the
left
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Positively Skewed
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The data peak to the left and trail off to the
right
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Example
Positively skewed
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Example
Symmetric distribution
Most students receive about $8
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Example
Positively skewed distribution
This indicates that most workers do up to 3 hours of
exercise per week. Very few do more and the most
time spent is 8 hours.