Question

3, 9, 4, 4, 4, 9, 9 : Calculate the value of the sample standard deviation. Round your answer to one decimal place.

Answer 1

In order to calculate the standard deviation, we can use the following formula:

$\sigma=\sqrt[]{\frac{\sum ^N_i(x_i-\mu)^2}{N}}$

Where μ is the average of the sample and N is the number of elements.

So, calculating the average, we have:

$\mu=\frac{3+9+4+4+4+9+9}{7}=\frac{42}{7}=6$

Now, using N = 7 and calculating the standard deviation, we have:

$\begin{gathered} \sigma=\sqrt[]{\frac{(3-6)^2+(9-6)^2+(4-6)^2+(4-6)^2+(4-6)^2+(9-6)^2+(9-6)^2}{7}} \\ \sigma=\sqrt[]{\frac{9+9+4+4+4+9+9}{7}} \\ \sigma=\sqrt[]{\frac{48}{7}} \\ \sigma=2.6 \end{gathered}$

So the standard deviation is 2.6.