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

Paulkenyo

Paulkenyo

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2022-08-19

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

Answer & Explanation

Donovan Burns

Donovan Burns

Beginner2022-08-20Added 4 answers

The mean (average) and standard deviations can be obtained directly from a calculator in stat mode. This yields
x ¯ = 1 n 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 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 and σ x = 280
The range is simplify x m a x x m i n = 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,-20,142,147,164,169,212,234,261,261,272,292,1100}
The middle data value is hence the median, and is 169

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