Question

Find sd. The differences between two sets of dependent data are 0.4, 0.24, 0.22, 0.26, 0.34. Round to the nearest hundredth.

Answer 1

The standard deviation of the data sample give the degree of spread of the data. Hence, the standard deviation of the data is 0.08

The sample standard deviation is defined as :

• $\sqrt {\frac{(x - \mean)^{2} }{n-1}}$

The mean :

• $\mean = \frac{ x_{1} + x_{2} +... + x_{n}}{n}$

$\mean = \frac{0.4 + 0.24 + 0.22 + 0.26 + 0.34}{5} = 0.292$

The Variance :

$\sqrt {\frac{(0.4 - 0.292)^{2} + (0.24 - 0.292)^{2} + (0.22 - 0.292)^{2} + (0.26 - 0.292)^{2} + (0.34 - 0.292)^{2}}{5 - 1}} = 0.00572$

The standard deviation :

$\sqrt {\frac{(x - \mean)^{2} }{n-1}}$

$\sqrt {0.00572} = 0.0756$

Therefore, the standard deviation of the data sample is 0.08.

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