Question

in the data set below, what is the standard deviation? 8 7 3 5 3 if the answer is a decimal, round it to the nearest tenth. standard deviation (σ):

Explanation:

Step1: Calculate mean

$\mu = \frac{8+7+3+5+3}{5} = 5.2$

Step2: Compute squared differences

$(8-5.2)^2=7.84$, $(7-5.2)^2=3.24$, $(3-5.2)^2=4.84$, $(5-5.2)^2=0.04$, $(3-5.2)^2=4.84$

Step3: Find variance

$\sigma^2 = \frac{7.84+3.24+4.84+0.04+4.84}{5} = 4.16$

Step4: Calculate standard deviation

$\sigma = \sqrt{4.16} \approx 2.0$

Answer:

2.0