Question

Calculate the standard deviation and variance of the given random sample data. Round to two decimal places. Can you please help me because all of the tutors are getting the same answer but its saying its wrong on my homework

Answer 1

We will have the following:

First, we remember:

*Standard deviation:

$\sigma=\sqrt{\frac{\Sigma\left(x_i-\mu\right)^2}{N}}$

*Variance:

$S^2=\frac{\Sigma\left(x_i-\mu\right)^2}{N-1}$

Now, we will have that:

First, we calculate the mean of the data set given, that is:

$\mu=\frac{3.7+4.4+4.9+13.5+18.1+19+19.9+24.6}{8}\Rightarrow\mu=13.5125$

Now, we will calculate:

*Standard deviation:

$\sigma=\sqrt{\frac{\Sigma\left(x_i-13.5125\right)^2}{8}}\Rightarrow\sigma=8.180017$

*Variance:

$S^2=\frac{\Sigma\left(x_i-13.5125\right)^2}{8-1}\Rightarrow S^2=66.912679$

So, the standard deviation and variance are approximately 8.18 and 66.9 respectively.