Question

find the standard deviation of the data set (as a population) below. round your answer to the nearest hundredths place if applicable.
3, 5, 3, 2, 2
show your work here
enter your answer

Explanation:

Step1: Calculate the mean

The data set is $3,5,3,2,2$. The mean $\mu=\frac{3 + 5+3+2+2}{5}=\frac{15}{5}=3$.

Step2: Calculate the squared - differences

For $x_1 = 3$, $(x_1-\mu)^2=(3 - 3)^2=0$; for $x_2 = 5$, $(x_2-\mu)^2=(5 - 3)^2=4$; for $x_3 = 3$, $(x_3-\mu)^2=(3 - 3)^2=0$; for $x_4 = 2$, $(x_4-\mu)^2=(2 - 3)^2=1$; for $x_5 = 2$, $(x_5-\mu)^2=(2 - 3)^2=1$.

Step3: Calculate the variance

The variance $\sigma^{2}=\frac{(x_1-\mu)^2+(x_2-\mu)^2+(x_3-\mu)^2+(x_4-\mu)^2+(x_5-\mu)^2}{n}=\frac{0 + 4+0+1+1}{5}=\frac{6}{5}=1.2$.

Step4: Calculate the standard deviation

The standard deviation $\sigma=\sqrt{\sigma^{2}}=\sqrt{1.2}\approx1.0954\approx1.10$.

Answer:

$1.10$