untchick04tm

2022-01-17

How do you calculate the standard deviation of 3.4, 6.1, 7.3, 4.5, 2.3, 4.4, 9.4, 3.4, 2.3, 7.2?

zesponderyd

Explanation:
Data:
{3.4,6.1,7.3,4.5,2.3,4.4,9.4,3.4,2.3,7.2}=50.3
Mean: $\frac{50.3}{10}=5.03$
Variance is average of the squared differences from the Mean.
Variance : ${\sigma }^{2}=\frac{1}{10}\cdot \left({\left(3.4-5.03\right)}^{2}+{\left(6.1-5.03\right)}^{2}+{\left(7.3-5.03\right)}^{2}$
$+{\left(4.5-5.03\right)}^{2}+{\left(2.3-5.03\right)}^{2}+{\left(4.4-5.03\right)}^{2}+{\left(9.4-5.03\right)}^{2}$
$+{\left(3.4-5.03\right)}^{2}+{\left(2.3-5.03\right)}^{2}+{\left(7.2-5.03\right)}^{2}\right)=\frac{1}{10}\cdot 51.001=5.1001$
Standard Deviation is the square root of Variance,
Standard deviation : $\sigma =\sqrt{5.1001}=2.25834\approx 2.26\left(2dp\right)$

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