gabriella asked 5 of her hundreds of coworkers how much storage space they were currently using on their…

gabriella asked 5 of her hundreds of coworkers how much storage space they were currently using on their computer. here are their responses (in gigabytes): 4, 8, 8, 9, 11 the mean of these amounts is $\bar{x}=8$ gigabytes. what is the standard deviation? round your answer to two decimal places. $s_xapprox$ gigabytes

gabriella asked 5 of her hundreds of coworkers how much storage space they were currently using on their computer. here are their responses (in gigabytes): 4, 8, 8, 9, 11 the mean of these amounts is $\bar{x}=8$ gigabytes. what is the standard deviation? round your answer to two decimal places. $s_xapprox$ gigabytes

Answer

Explanation:

Step1: Calculate squared - differences

For (x_1 = 4), ((x_1-\bar{x})^2=(4 - 8)^2=(-4)^2 = 16) For (x_2 = 8), ((x_2-\bar{x})^2=(8 - 8)^2=0^2 = 0) For (x_3 = 8), ((x_3-\bar{x})^2=(8 - 8)^2=0^2 = 0) For (x_4 = 9), ((x_4-\bar{x})^2=(9 - 8)^2=1^2 = 1) For (x_5 = 11), ((x_5-\bar{x})^2=(11 - 8)^2=3^2 = 9)

Step2: Calculate variance

The formula for the sample variance (s^{2}=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}), where (n = 5), (\sum_{i=1}^{5}(x_i-\bar{x})^2=16 + 0+0 + 1+9=26). So (s^{2}=\frac{26}{5 - 1}=\frac{26}{4}=6.5)

Step3: Calculate standard - deviation

The standard deviation (s=\sqrt{s^{2}}), so (s=\sqrt{6.5}\approx2.55)

Answer:

(2.55)