Question

suppose you made 5 measures of your walking stride and got the following values: 0.81 m, 0.87 m, 0.79 m, 0.84 m, and 0.83 m. what is the standard deviation (in meters) of this sample? you may either do this by hand or use your favorite math tool.

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{0.81 + 0.87+0.79+0.84+0.83}{5}=\frac{4.14}{5}=0.828$

Step2: Calculate the squared - differences

$(0.81 - 0.828)^2=(-0.018)^2 = 0.000324$
$(0.87 - 0.828)^2=(0.042)^2=0.001764$
$(0.79 - 0.828)^2=(-0.038)^2 = 0.001444$
$(0.84 - 0.828)^2=(0.012)^2=0.000144$
$(0.83 - 0.828)^2=(0.002)^2=0.000004$

Step3: Calculate the variance

The variance $s^{2}=\frac{0.000324 + 0.001764+0.001444+0.000144+0.000004}{5 - 1}=\frac{0.00368}{4}=0.00092$

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{0.00092}\approx0.0303$

Answer:

$0.0303$