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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