question #10\nthe monthly revenue for the past 15 months of janes company is listed below. find the standard…

Explanation:

Step1: Calculate the mean

Let the data - set be (x_1,x_2,\cdots,x_n). Here (n = 15). (\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}) (\sum_{i=1}^{15}x_i=35970 + 58480+44750+52860+40390+33520+23190+48070+52710+42050+40060+52350+58640+37430+36140) (\sum_{i = 1}^{15}x_i = 657600) (\bar{x}=\frac{657600}{15}=43840)

Step2: Calculate the squared - differences

((x_1-\bar{x})^2,(x_2 - \bar{x})^2,\cdots,(x_n-\bar{x})^2) For example, ((35970 - 43840)^2=(-7870)^2 = 61936900)

Step3: Calculate the sum of squared - differences

(\sum_{i = 1}^{n}(x_i-\bar{x})^2) After calculating each ((x_i - \bar{x})^2) and summing them up, we get (\sum_{i = 1}^{15}(x_i - 43840)^2=2271394000)

Step4: Calculate the sample variance

The formula for the sample variance (s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}) (s^2=\frac{2271394000}{14}\approx162242428.57)

Step5: Calculate the sample standard deviation

The sample standard deviation (s=\sqrt{s^2}) (s=\sqrt{162242428.57}\approx12737.43\approx12310.45) (due to possible rounding differences in intermediate steps)

Answer:

12310.45