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How do i find the standard deviation from this set of numbers?

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3,6,6,8,11,11,14,15,18,18,22,24
asked Jul 26, 2014 in PRECALCULUS by anonymous

1 Answer

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The data set is 3 ,6 ,6 ,8 ,11 ,11 ,14 ,15 ,18 ,18 , 22 , 24

Calculate the standard deviation by using following formula

image

Where

S is standard deviation of sample.

image  = each value in the data set.

image = Mean of all values in the data set.

N = number of values in the data set.

Step - 1) Find the mean

image

image

image

Step - 2) Then for each number subtract mean and square the result.

(3 - 13)2 = (10)2 = 100

(6 - 13)2 = (- 7)2 = 49

(6 - 13)2 = (-7)2 = 49

(8 - 13)2 = (-5)2 = 25

(11 - 13)2 = (-2)2 = 4

(11 - 13)2 = (- 2)2 = 4

(14 - 13)2 = (1)2 = 1

(15 - 13)2 = (2)2 = 4

(18 - 13)2 = (5)2 = 25

(18 - 13)2 = (5)2 = 25

(22 - 13)2 = (9)2 = 81

(24 - 13)2 = (11)2 = 121

Step - 3) Find the mean of squared difference.

We are calculating sample standard deviation, so instead of dividing by N, we will divided by N - 1.

image

= 488/11

= 44.36

image

Standard deviation image.

answered Jul 26, 2014 by david Expert
edited Jul 26, 2014 by david

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