Question

Three randomly chosen colorado students were asked how many times they went rock climbing last month. their replies were 5, 6, 7. the standard deviation is:

Answer 1

To calculate the standard deviation we use the formula:
Where (x-X)² is the squared difference from the mean, and "n" is the number of samples.

First we calculate the mean, which is the sum of the samples divided by the number of samples:
$\frac{5+6+7}{3} = 3$

Then we calculate the sum of the squared differences from the mean:
$(5-6) ^{2} +(6-6) ^{2} +(7-6) ^{2}$
$(-1) ^{2} +(0) ^{2} +(1) ^{2} =2$

Now we can replace the values in the formula to get:
$s= \sqrt{ \frac{2}{3-1} }$
$s= \sqrt{ \frac{2}{2} }$
$s=1$

The standard deviation of the sample is 1