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NSW Y12 Maths - Advanced Descriptive Statistics Standard Deviation

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Standard Deviation Theory

There are four measures of spread: the range, the interquartile range, the variance and the standard deviation.\\ The range \(=\) maximum value - minimum value.\\ The interquartile range \(IQR\) represents the middle \(50 \%\) of an ordered dataset.\\ The variance is the square of the standard deviation. \(\left(\sigma^2\right)\)\\ The population standard deviation \(\sigma_N=\sqrt{\dfrac{\sum(x-\mu)^2}{n}}\) where \(\mu=\) mean and \(n\) is the number in the data set.\\ The sample standard deviation \(\sigma_{N-1}=\sqrt{\dfrac{\sum(x-\mu)^2}{n-1}}\) Calculating the variance and standard deviation by hand is complicated and it is better to calculate using technology.\\ \textbf{Example 1}\\ Given the scores: \(2,8,8,9,9,9,10,10,11,18\). Determine the interquartile range and the sample standard deviation\\ \textbf{Example 1 solution}\\ $\begin{aligned} &\begin{array}{ccccccccc} &&&&\textcolor{red}Q_{2}&&&&\\ 2&8&8&9&9\ 9&10&10&11&18\\ &&\textcolor{red}\downarrow&&&&\textcolor{red}\downarrow&&\\ &&\textcolor{red}Q_{2}&&&&\textcolor{red}Q_{2}&&\\ \end{array}\\ &\begin{aligned} IQR &=10-8 \quad \sigma_{N}-1=3.9 \text { (by calculator) } \\ &=2 \end{aligned} \end{aligned}$\\

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Videos

Videos relating to Standard Deviation.

  • Standard Deviation - Video - Standard Deviation - Explained and Visualized

  • Standard Deviation - Video - How To Calculate The Standard Deviation

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