Further MathsFurther Maths

Univariate DataUnivariate Data

Univariate meaning: One variable. Univariate meaning: One variable. One quantity that changes. For One quantity that changes. For example, number of cars sold by a example, number of cars sold by a car salesmancar salesman

Type of data: Numerical and Type of data: Numerical and Categorical data. Categorical data.

Interpreting the data: Discrete and Interpreting the data: Discrete and continuouscontinuous

Stem PlotsStem Plots One way of displaying data-how the One way of displaying data-how the

data is distributed.data is distributed. Use this method if there are 50 (or Use this method if there are 50 (or

less) observationsless) observations Consist of two parts - a stem and a Consist of two parts - a stem and a

leaf, is always the last digit.leaf, is always the last digit. Important!!!! Must always arrange Important!!!! Must always arrange

the data in ascending first (not the data in ascending first (not necessarily if using the graphic necessarily if using the graphic calculator)calculator)

The stem may be broken into halves The stem may be broken into halves or fifths if the data are bunched up or fifths if the data are bunched up closely.closely.

The stem plot need to include a key The stem plot need to include a key (similarly like a legend)(similarly like a legend)

Frequency histograms, dot Frequency histograms, dot plots and bar chartsplots and bar charts

Other alternatives to display data, but Other alternatives to display data, but larger data sets (50 or over larger data sets (50 or over observations)observations)

Frequency histograms and bar charts Frequency histograms and bar charts are like column graphs, very similar are like column graphs, very similar except that one is separated by a except that one is separated by a small equally space.small equally space.

Note: This course relies reasonably on Note: This course relies reasonably on the use of the graphic calculator – the use of the graphic calculator – LEARN HOW TO USE IT!!!!LEARN HOW TO USE IT!!!!

Segmented bar chartsSegmented bar charts

A single bar to represent all the data A single bar to represent all the data being studied.being studied.

The information is presented as The information is presented as percentages and so the total bar percentages and so the total bar length represents 100% of the data.length represents 100% of the data.

Describing the shape of stem Describing the shape of stem plots and histogramsplots and histograms

Symmetric distributionsSymmetric distributions

Skewed distributionsSkewed distributions

DistributionDistribution The spread of the dataThe spread of the data

Symmetric distribution (single peak and the Symmetric distribution (single peak and the data trial off on both sides of this peak in data trial off on both sides of this peak in roughly the same fashion)roughly the same fashion)

Negatively Skewed Negatively Skewed The data peak to the right and trial off The data peak to the right and trial off

to the leftto the left

Positively SkewedPositively Skewed The data peak to the left and trail off to The data peak to the left and trail off to

the rightthe right

ExampleExample

Positively skewed

ExampleExample

Symmetric distribution

Most students receive about $8

ExampleExample

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.