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?
standard deviation:
$s = \sqrt{\frac{\left(x_1 - \bar{x}\
ight)^2 + \left(x_2 - \bar{x}\
ight)^2 + \dots + \left(x_n - \bar{x}\
ight)^2}{n - 1}}$
\bigcirc 0
\bigcirc 4.4
\bigcirc 5.2
\bigcirc 26.7

Explanation:

Step1: Calculate the mean (\(\bar{x}\))

The data set is \(13, 17, 9, 21\). The number of data points \(n = 4\).
The mean \(\bar{x}=\frac{13 + 17 + 9 + 21}{4}=\frac{60}{4}=15\).

Step2: Calculate the squared differences

For \(x_1 = 13\): \((13 - 15)^2=(-2)^2 = 4\)
For \(x_2 = 17\): \((17 - 15)^2=(2)^2 = 4\)
For \(x_3 = 9\): \((9 - 15)^2=(-6)^2 = 36\)
For \(x_4 = 21\): \((21 - 15)^2=(6)^2 = 36\)

Step3: Sum the squared differences

Sum \(= 4 + 4 + 36 + 36 = 80\)

Step4: Calculate the variance

Variance \(s^2=\frac{80}{4 - 1}=\frac{80}{3}\approx26.67\)

Step5: Calculate the standard deviation

Standard deviation \(s=\sqrt{\frac{80}{3}}\approx\sqrt{26.67}\approx5.2\)

Answer:

5.2