Consider the data set ( 2, 3, 4, 6, 9)

Question

(a) Use the defining formula to compute the sample standard deviation s. (Round your answer to two decimal places.)

(b) Use the defining formula to compute the population standard deviation 𝜎. (Round your answer to two decimal places.)

Answer 1

X deviation deviation^2 X^2

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2 -2.8 7.84 4

3 -1.8 3.24 9

4 -0.8 0.64 16

6 1.2 1.44 36

9 4.2 17.64 81

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24 0 30.8 146

Mean = 24/5 = 4.8

variance by defintion = sum of dev^2 = 30.8

variance by shortcut formula = sum of X^2 - N*mean^2

= 146 - 5* 4.8^2

= 146 - 115.2

= 30.8

Sample variance, divides by N-1 ---> 30.8 / (5-1)

= 30.8 / 4

= 7.7

So the sample standard deviation is sqrt(7.7) = 2.7748873851023215893479457892222...

which is rounded to 2.77

Population variance, divides by N ---> 30.8/5 = 6.16

So the population standard deviation is sqrt(6.16) = 2.4819347291981713192266483910899

= 2.48