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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


  • 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.


Picture 2

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


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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