Question

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

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:

\(2.55\)