Question

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

Answer 1

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

`barx=1/nsum_(i=1)^nx_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 `barx=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 and sigma_x=280`

The range is simply `x_(max)-x_(min)=1100-(-90)=1190`.

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

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

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