what is the standard deviation of the following sample: 5, 17, 12, 11, 10, 14, 8?\nhint: use the…

what is the standard deviation of the following sample: 5, 17, 12, 11, 10, 14, 8?\nhint: use the following.\ns = \\sqrt{\\frac{\\sum (x - \\bar{x})^2}{n - 1}}\n3.62\n15.33\n3.92\n13.14\n3.76

what is the standard deviation of the following sample: 5, 17, 12, 11, 10, 14, 8?\nhint: use the following.\ns = \\sqrt{\\frac{\\sum (x - \\bar{x})^2}{n - 1}}\n3.62\n15.33\n3.92\n13.14\n3.76

Answer

Explanation:

Step1: Calculate the mean

The data set is (5, 17, 12, 11, 10, 14, 8). The mean (\bar{x}=\frac{5 + 17+12+11+10+14+8}{7}=\frac{77}{7} = 11).

Step2: Calculate ((x - \bar{x})^2) for each data - point

For (x = 5): ((5 - 11)^2=(-6)^2 = 36) For (x = 17): ((17 - 11)^2=6^2 = 36) For (x = 12): ((12 - 11)^2=1^2 = 1) For (x = 11): ((11 - 11)^2=0^2 = 0) For (x = 10): ((10 - 11)^2=(-1)^2 = 1) For (x = 14): ((14 - 11)^2=3^2 = 9) For (x = 8): ((8 - 11)^2=(-3)^2 = 9)

Step3: Calculate (\sum(x - \bar{x})^2)

(\sum(x - \bar{x})^2=36 + 36+1+0+1+9+9=92)

Step4: Calculate the standard deviation

We know (n = 7), and the formula for sample standard deviation (s=\sqrt{\frac{\sum(x - \bar{x})^2}{n - 1}}) (s=\sqrt{\frac{92}{7 - 1}}=\sqrt{\frac{92}{6}}\approx\sqrt{15.33}\approx3.92)

Answer:

3.92