Measures of Spread

• Interquartile Range = IQR = $Q_3\ -\ Q_1$
• What's the advantage of the interquartile range?

  ignores extreme values
• Interpercentile range:

  $P_n$ to $P_{n+x}$ = $P_{n+x}\ -\ P_n$

  
  

  eg. 10th to 90th IPR = $P_{90}\ -\ P_{10}$
• Variance, $\sigma^2$ :

  $\sigma^2$ = $\frac{\sum_{ }^{ }x^2}{N}\ -\ \overline{x}^{\ 2}$

  Mnemonic: MSMSM
• Variance equation for grouped data:

  
  

  $\sigma^2$ = $\frac{\sum_{ }^{ }fx^2}{\sum_{ }^{ }f}-\overline{x}^2$
• Is $\sum_{ }^{ }fx^2$ the same as $\left(\sum_{ }^{ }fx\right)^2$ ?


  No
• Standard deviation ( $\sigma$ ) is the square root of the variance ( $\sigma^2$ )