Question 1154331
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Original set = {59, 143, 80, 69, 176, 86, 160, 65, 152, 184}
Sorted set = {59, 65, 69, 80, 86, 143, 152, 160, 176, 184}
min = 59 and max = 184


mu = mean = 117
sigma = standard deviation = 47


1 standard deviation from the mean
L = lower bound = mu - 1*sigma = 117-1*47 = 70
U = upper bound = mu + 1*sigma = 117+1*47 = 164


Ask yourself: Do all of the data values fall within the interval {{{70 <= x <= 164}}} (this is in the form {{{L <= x <= U}}})? The answer is 'no' because 59, 65, 69, 176, and 184 are outside this range.


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2 standard deviations from the mean
L = lower bound = mu - 2*sigma = 117-2*47 = 23
U = upper bound = mu + 2*sigma = 117+2*47 = 211


The interval is now {{{23 <= x <= 211}}}. Ask a similar question: Do all of the data values fall within the range {{{23 <= x <= 211}}}? The answer is 'yes'. This is because L = 23 is smaller than the min = 59, while U = 211 is larger than the max = 184.


Final Answer: <font size=4 color=red>2 standard deviations</font>
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