Question

Omar recorded the number of hours he worked each week for a year. Below is a random sample that he took from his data. 13, 17, 9, 21 What is the standard deviation for the data?

Answer 1

standard deviation=4.47

Explanation:

We have to find the standard deviation of the data set:

13 17 9 21

Now we calculate the mean of the data .

We know that mean is the average of the data values and is calculated as:

`Mean=(13+17+9+21)/(4)\\ \\Mean=(60)/(4)\\\\Mean=15`

Now we find the difference of each data point from the mean as:

Deviation:

13-15=-2

17-15=2

9-15=-6

21-15=6

Now we have to square the above deviations we obtain:

4 4 36 36

now we calculate the mean of the above sets:

`variance=(4+4+36+36)/(4)\\ \\Variance=(80)/(4)\\\\Variance=20`

now standard deviation is the positive square root of variance

so, standard deviation=√(20)=4.47