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

1 Answer
Trevor Ryan.
Nov 6, 2015

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.

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