A+ » VCE » Further Maths U3 & 4 Master Notes » A1 Data Analysis » FM Numerical Data

# FM Numerical Data

## 2.1 Response and Explanatory Variables

### Explanatory Variable

• The explanatory variable (EV) is the variable used to explain or predict another variable (the response variable).
• By convention, the explanatory variable is plotted along the x-axis of a graph, if it is numerical.

### Response Variable

• The response variable (RV) is the variable which is explained or predicted by the explanatory variable.
• By convention, the response variable is plotted along the y-axis of a graph, if it is numerical.

Note: both explanatory and response variables can be either categorical or numerical variables.

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## 1.5 Basic Statistical Concepts

### Mean

• The mean of a numerical distribution is found by summing up the values of all individual data points, then dividing by the number of data points.
• It is represented by either a capital letter with a bar drawn above it, or the Greek symbol mu (µ):

\bar{X}=\frac{\sum_{i=1}^{N} x_{i}}{N}

Where N is the total number of data points, and represents the i’th datapoint.

Note: the symbol \Sigma is short for “sum of”, so \sum_{i=1}^{N} x_{i} represents the sum of all individual data points (from datapoint 1, to datapoint N)

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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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## 1.1 Overview of Data Types

### Categorical Data

• Data which is sorted into groups is considered categorical data

Nominal Data

• Categorical data with no hierarchy (i.e. one category is not “greater than” another) is considered nominal data

Example

Eye colour can be considered a nominal data type as the data (each person’s eye colour) can be placed into groups and there is no hierarchy

Ordinal Data

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