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Chapter 1   One Numerical Variable

1.1   Graphical displays

1.1.1   Stem and leaf plots

In the two exercises on this page, you will drag leaves to form stem and leaf plots from a list of values. The second exercise creates stem and leaf plots with split stems.

1.1.2   Stacked dot plots

This exercise asks you to drag the final two crosses of a stacked dot plot into the correct places of the display.

1.1.3   Box plots

The exercises on this page involve drawing box plots from sorted lists of values. For the second exercise, 'outliers' must be separately identified.

1.1.4   Histograms

In this page, you will draw histograms of different data sets.

1.1.5   Shape of a box plot

The exercises on this page involve matching the shape of box plots to the corresponding dot plots.

1.1.6   Histogram areas and proportions

The two exercises in this page ask you to use the shape of a histogram to find the proportion of values in a given range. The first exercise shows the number of values in each class, but the second requires the histogram area to be estimated 'by eye'.

1.1.7   Information from distributions

In this exercise, you will interpret what distributions with symmetry, skewness, clusters or outliers tell you about the data.

1.2   Describing centre and spread

1.2.1   Ideas of centre and spread

In this exercise, you should summarise the difference between two distributions in terms of their different centres and spreads.

1.2.2   Mean and median

An exercise requests estimates of the mean and median from different skew and symmetric stacked dot plots.

1.2.3   Standard deviation from graph

The first exercise asks for a rough 'guess' at the standard deviation of data sets from a stacked dot plot. The second exercise is similar but displays the data as a histogram or box plot.

1.2.4   Standard deviation from general knowledge

In this exercise, general knowledge about the type of measurement is enough to roughly guess the value of the standard deviation.

1.2.5   Rough graph from mean and st devn

The mean and standard deviation of a data set should give you a good idea of the likely distribution of values. The first exercise in this page asks you to sketch a stacked dot plot to match a given mean and standard deviation. In the second, a histogram should be drawn.

1.2.6   Clusters and outliers (advanced)

The two exercises on this page ask the effect of combining different groups of values or adding an outlier on the mean and standard deviation.

1.3   Proportions and percentiles

1.3.1   Cumulative distribution functions

In this page, you will draw cumulative distribution functions based for various data sets. In the first exercise, the cdf is drawn from the individual data values (displayed as a dot plot); in the second, the values are grouped into classes (as a histogram).

1.3.2   Shape of the cumulative distribution function

In the two exercises on this page, you should identify which of a set of cumulative distribution functions matches each of a set of dot plots or histograms.

1.3.3   Percentages, rates and return periods

In this exercise, a proportion should be expressed as a percentage, a rate per x values, or a rate of once per y values (return period)

1.3.4   Percentages from cumulative distn function

An exercise gives practice at finding proportions from the cumulative distribution function of real climatic data.

1.3.5   Rates and return periods from c.d.f.

This is similar to the exercise on the previous page but asks for a mixture of percentages, rates and return periods.

1.3.6   Percentiles

In this page, two exercises give practice at finding percentiles, again based on the cumulative distribution function of climatic data.

1.4   Transformations

1.4.1   Linear transformations

In this exercise, a data set is shown and a question is asked about the proportion of values that are less than a cutoff which is expressed in different units.

1.4.2   Mean and st devn after linear transformations

The exercise on this page asks for the mean and standard deviation of a data set after linear transformation.

1.4.3   Nonlinear transformations

In this exercise, you are asked to identify which of three nonlinearly transformed dot plots correspond to square, log and square root transformations of a data set.