Question

Calculate the standard deviation of the data shown, to two decimal places

x
14.5
17.7
25.2
2.5
24.5
16.8
10.2
15.5

Answer 1

First, add all given numbers:2.5 + 10.2 + 14.5 + 15.5 + 16.8 + 17.7 + 24.5 + 25.2 = 126.9

next, square the total, and then divided the number of items in the data set126.9 x 126.9 = 16103.61
16103.61 / 8 = 2012.95125

take original numbers from step 1, squared them individually this time, and added them all up:

(2.5 x 2.5) + (10.2 x 10.2) + (14.5 x 14.5) + (15.5 x 15.5) + (16.8 x 16.8) + (17.7 x 17.7) + (24.5 x 24.5) + (25.2 x 25.2) = 2391.6099999999997

subtract the amount in step 2 from the amount in step 3:2391.6099999999997 - 2012.95125 = 378.6587499999996

subtract 1 from the number of items in my data set:8 - 1 = 7

divide the number in step 4 by the number in step 5:378.6587499999996 / 7 = 54.094107142857084
this is Variance.

now take square root to get standard deviation.

√(54.094107142857084) = 7.354869621064474
This is Standard Deviation

on rounding we get s.d.= 7.35

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