# What are the range, median, mean, and standard deviation of: {212, 142, 169, 234, 292, 261, 147, 164, 272, -20, -26, -90, 1100}?

Nov 6, 2015

The mean (average) and standard deviations can be obtained directly from a calculator in stat mode. This yields

$\overline{x} = \frac{1}{n} {\sum}_{i = 1}^{n} {x}_{i} = 219 , 77$

Strictly speaking, since all the data points in the sample space are integers, we should express the mean also as an integer to the correct number of significant figures, ie $\overline{x} = 220$.

The 2 standard deviations, depending on whether you want the sample or population standard deviation is, also rounded to the nearest integer value,

${s}_{x} = 291 \mathmr{and} {\sigma}_{x} = 280$

The range is simply ${x}_{\max} - {x}_{\min} = 1100 - \left(- 90\right) = 1190$.

To find the median, we need to arrange the sample space of points in ascending numerical order to find the middle value.

$X = \left\{- 90 , - 26 , - 20 , 142 , 147 , 164 , 169 , 212 , 234 , 261 , 272 , 292 , 1100\right\}$.

The middle data value is hence the median, and is $169$.