Question

A family goes grocery shopping every week. in a month the costs of the groceries are $72.42, $91.50, $58.99, and $69.02. 5. what is the mean? 6. what is the standard devi

Answer 1

1) Mean
The mean is given by the sum of the data divided by the number of data (4, in this case):
$\mu = \frac{1}{N} \sum x_i = \frac{1}{4}(72.42+91.50+58.99+69.02) = \frac{291.93}{4}=72.98$

2) Standard deviation
The standard deviation is given by:
$\sigma = \sqrt{ \frac{1}{N} \sum (x_i-\mu)^2 }$
where $\mu$ is the mean, that we already found at point 1), and N=4. Substituting data, we have:
$\sigma = \sqrt{ \frac{1}{4} ((-0.56)^2+(18.52)^2+(-13.99)^2+(-3.96)^2) } =$
$= \sqrt{ \frac{1}{4} (554.71)} = \sqrt{138.68} =11.78$