Example 1.27

EXAMPLE 1.27 Standard Deviation for Time to Start a Business

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In Example 1.22 (page 24), we found that the mean time to start a business for the 24 countries in our data set was 16.3 days. Here, we keep an extra two digits $(\bar{x} = 16.292)$ to make sure that our intermediate calculations are accurate. When we are done, we will round the standard deviation in the same way that we rounded the mean, giving one digit after the decimal. We organize the arithmetic in a table.

Page 32

Observations $x_{i}$	Deviations $x_{i} - \bar{x}$	Squared deviations ${(x_{i} - \bar{x})}^{2}$
16	$16 - 16.292 = - 0.292$	${(- 0.292)}^{2} = 0.085$
4	$4 - 16.292 = - 12.292$	${(- 12.292)}^{2} = 151.093$
...	...= ...	...= ...
17	$17 - 6.292 = 0.708$	${(0.708)}^{2} = 0.501$
	$sum = - 0.008$	$sum = 4614.96$

The variance is the sum of the squared deviations divided by 1 less than the number of observations:

$s^{2} = \frac{4614.96}{23} = 200.65$

The standard deviation is the square root of the variance:

$s = \sqrt{200.65} = 14.2 days$