Question

the following data points are last weeks revenues (in thousands of dollars) for the 5 hermans hoagies locations. 5, 6, 5, 10, 9. find the standard deviation of the data set. round your answer to the nearest hundredth. thousand dollars show calculator

Explanation:

Step1: Calculate the mean

The data set is \(5,6,5,10,9\). The mean \(\bar{x}=\frac{5 + 6+5+10+9}{5}=\frac{35}{5}=7\).

Step2: Calculate the squared - differences

\((5 - 7)^2=(-2)^2 = 4\), \((6 - 7)^2=(-1)^2 = 1\), \((5 - 7)^2=(-2)^2 = 4\), \((10 - 7)^2=3^2 = 9\), \((9 - 7)^2=2^2 = 4\).

Step3: Calculate the variance

The variance \(s^{2}=\frac{4 + 1+4+9+4}{5}=\frac{22}{5}=4.4\).

Step4: Calculate the standard deviation

The standard deviation \(s=\sqrt{4.4}\approx2.10\).

Answer:

\(2.10\)