# 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?

Aug 2, 2017

Standard deviation is $2.26 \left(2 \mathrm{dp}\right)$

#### Explanation:

Data: $\left\{3.4 , 6.1 , 7.3 , 4.5 , 2.3 , 4.4 , 9.4 , 3.4 , 2.3 , 7.2\right\} = 50.3$

Mean: $\frac{50.3}{10} = 5.03$

Variance is average of the squared differences from the Mean.

Variance : sigma^2 = 1/10* ((3.4-5.03)^2 + (6.1-5.03)^2 +(7.3-5.03)^2

$+ {\left(4.5 - 5.03\right)}^{2} + {\left(2.3 - 5.03\right)}^{2} + {\left(4.4 - 5.03\right)}^{2} + {\left(9.4 - 5.03\right)}^{2}$

+(3.4-5.03)^2+(2.3-5.03)^2+(7.2-5.03)^2) = 1/10 *51.001 = 5.1001

Standard Deviation is the square root of Variance,

Standard deviation : $\sigma = \sqrt{5.1001} = 2. 25834 \approx 2.26 \left(2 \mathrm{dp}\right)$