Question

question for the following set of data, find the sample standard deviation, to the nearest thousandth. 47, 41, 46, 39, 38, 38, 45, 39 copy values for calculator open statistics calculator answer attempt 1 out of 2

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{47 + 41+46+39+38+38+45+39}{8}=\frac{333}{8}=41.625$

Step2: Calculate the squared - differences

$(47 - 41.625)^2=(5.375)^2 = 28.890625$
$(41 - 41.625)^2=(- 0.625)^2=0.390625$
$(46 - 41.625)^2=(4.375)^2 = 19.140625$
$(39 - 41.625)^2=(-2.625)^2 = 6.890625$
$(38 - 41.625)^2=(-3.625)^2 = 13.140625$
$(38 - 41.625)^2=(-3.625)^2 = 13.140625$
$(45 - 41.625)^2=(3.375)^2 = 11.390625$
$(39 - 41.625)^2=(-2.625)^2 = 6.890625$

Step3: Calculate the sum of squared - differences

$S=\sum_{i = 1}^{8}(x_i-\bar{x})^2=28.890625+0.390625+19.140625+6.890625+13.140625+13.140625+11.390625+6.890625 = 99.8625$

Step4: Calculate the sample variance

The sample variance $s^2=\frac{S}{n - 1}=\frac{99.8625}{8 - 1}=\frac{99.8625}{7}\approx14.26607$

Step5: Calculate the sample standard deviation

The sample standard deviation $s=\sqrt{s^2}=\sqrt{14.26607}\approx3.777$

Answer:

$3.777$