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: $s = sqrt{\frac{(x_1 - overline{x})^2+(x_2 - overline{x})^2+cdots+(x_n - overline{x})^2}{n - 1}}$ 0 4.4 5.2 26.7

Explanation:

Step1: Calculate the mean

$n = 4$, $x_1=13,x_2 = 17,x_3=9,x_4 = 21$. The mean $\bar{x}=\frac{13 + 17+9+21}{4}=\frac{60}{4}=15$.

Step2: Calculate the squared - differences

$(x_1-\bar{x})^2=(13 - 15)^2=(-2)^2 = 4$; $(x_2-\bar{x})^2=(17 - 15)^2=2^2 = 4$; $(x_3-\bar{x})^2=(9 - 15)^2=(-6)^2 = 36$; $(x_4-\bar{x})^2=(21 - 15)^2=6^2 = 36$.

Step3: Calculate the sum of squared - differences

$\sum_{i = 1}^{4}(x_i-\bar{x})^2=4 + 4+36+36=80$.

Step4: Calculate the variance

The variance $s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}=\frac{80}{4 - 1}=\frac{80}{3}\approx26.67$.

Step5: Calculate the standard deviation

The standard deviation $s=\sqrt{\frac{80}{3}}\approx5.2$.

Answer:

5.2