Question

calculate the variance for the data set. show all of your steps.
{4, 16, 21, 32, 11, 12}

Explanation:

Step1: Calculate the mean

$\bar{x}=\frac{4 + 16+21+32+11+12}{6}=\frac{96}{6}=16$

Step2: Calculate the squared - differences

$(4 - 16)^2=(-12)^2 = 144$
$(16 - 16)^2=0^2 = 0$
$(21 - 16)^2=5^2 = 25$
$(32 - 16)^2=16^2 = 256$
$(11 - 16)^2=(-5)^2 = 25$
$(12 - 16)^2=(-4)^2 = 16$

Step3: Calculate the variance

$S^2=\frac{144 + 0+25+256+25+16}{6}=\frac{466}{6}\approx77.67$

Answer:

$\frac{466}{6}\approx77.67$