omar recorded the number of hours he worked each week for a year. below is a random sample that he took from…

omar recorded the number of hours he worked each week for a year. below is a random sample that he took from his data.\n13, 17, 9, 21\nwhat is the standard deviation for the data?\nstandard deviation: $s = sqrt{\frac{(x_1-overline{x})^2+(x_2 - overline{x})^2+cdots+(x_n-overline{x})^2}{n - 1}}$\n0\n4.4\n5.2\n26.7

omar recorded the number of hours he worked each week for a year. below is a random sample that he took from his data.\n13, 17, 9, 21\nwhat is the standard deviation for the data?\nstandard deviation: $s = sqrt{\frac{(x_1-overline{x})^2+(x_2 - overline{x})^2+cdots+(x_n-overline{x})^2}{n - 1}}$\n0\n4.4\n5.2\n26.7

Answer

Explanation:

Step1: Calculate the mean

The data set is (13, 17, 9, 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}), where (n = 4). So (s^2=\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