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

mean =  60 / 4 = 15

13 - 15 = -2
17 - 15 =    2
9 - 15 = -6
21 - 15 = 6
Total of squares  =  4 + 4 + 36 + 36  =  80

because this is a sample we divide this by n - 1 ( = 3)

Standard deviation  =  sqrt (80/3)  = 5.16 answer

Answer 2

Answer:

standard deviation=4.47

Step-by-step 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:

$Mean=\dfrac{13+17+9+21}{4}\\ \\Mean=\dfrac{60}{4}\\\\Mean=15$

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:

$variance=\dfrac{4+4+36+36}{4}\\ \\Variance=\dfrac{80}{4}\\\\Variance=20$

now standard deviation is the positive square root of variance

so, standard deviation=√(20)=4.47