Question

the 5 participants in a weight - loss class lost the following weights (in pounds) after three weeks of dieting. 4, 3, 0, 0, 3. send data to calculator. assuming that these weights constitute an entire population, find the standard deviation of the population. round your answer to two decimal places. (if necessary, consult a list of formulas.)

Explanation:

Step1: Calculate the mean

The data set is \(4,3,0,0,3\). The mean \(\mu=\frac{4 + 3+0+0+3}{5}=\frac{10}{5}=2\).

Step2: Calculate the squared - differences

\((4 - 2)^2=4\), \((3 - 2)^2 = 1\), \((0 - 2)^2=4\), \((0 - 2)^2=4\), \((3 - 2)^2 = 1\).

Step3: Calculate the variance

The variance \(\sigma^{2}=\frac{4+1 + 4+4+1}{5}=\frac{14}{5}=2.8\).

Step4: Calculate the standard deviation

The standard deviation \(\sigma=\sqrt{2.8}\approx1.67\).

Answer:

\(1.67\)