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Measures of centre

The mean

  • The mean is the average of the data points. Can be calculated by: \[\bar{x} = \frac{\mbox{sum of all observations}}{\mbox{ total number of observations} }\]
  • The mean can also be denoted \(\bar{y}\).
  • Used for quantitative data. 
  • For example a nurse measured a patient’s temperature (in degrees Celcius) \(4\) times \( ( 37.2\), \(37.5\), \(37.1\), \(37.3)\), the mean temperature will be:
  • \begin{eqnarray*}
    \bar{x} &=& \frac{ \mbox{sum of all observations}}{\mbox{total number of observations} }\\
    &=&\frac{37.2+ 37.5+ 37.1+ 37.3}{4} \\
    &=& 37.275 \\
    &\approx& 37.3^\circ\mbox{C}
    \end{eqnarray*}

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