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# ACMGM029

## 2.4 Scatterplots and Association between Numerical Variables

### Scatterplots

• Scatterplots are used to visualise data with explanatory and response variables.
• They consist of an x-y axis with each datapoint represented as a dot above its x-value and to the right of its y-value.
• Scatterplots can be used to see relationships between variables. These relationships can be described in terms of form, direction and strength.

Example

### Form

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## 2.3 Relationships between Numerical and Categorical Variables

### Discussing Relationships between Numerical and Categorical Variables

• Begin with context: what does the data represent?
• Compare frequencies between the categories of the categorical dataset.
• Compare the numerical data corresponding to each category on the basis of shape, spread, centre and presence of outliers.

Note: if you cannot remember how to choose appropriate measures for centre and spread, revise the notes for 1.6 Describing Numerical Distributions.

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## 1.9 The Normal Distribution

### Overview of the Normal Distribution

• The normal distribution appears often in population and natural distributions.
• It is often referred to as the bell curve.
• Normal distributions are assumed to be perfectly symmetric.

Note: this is not always the case in practice, but it is an accurate approximation.

• A key characteristic of the normal distribution is that the mean and median are equal and correspond to the highest frequency
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## 1.4 Displaying Numerical Data

### Dot Plot

• Dot plots consist of a number line with each individual datapoint listed as a dot above it’s value. If multiple data points have the same value, they are placed in a column.

Example

### Stem Plot

• Stem plots are useful for displaying small to medium sized datasets.
• The leading term for each value is referred to as a stem and is placed on the left side of a vertical line.
• The following terms in each value are referred to as the leaf and are placed to the right of the line.
• Multiple data points can share a common stem, but each leaf must represent only one datapoint.

Note: you may also see stem plots referred to as stem and leaf plots.

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