chapter 3 quiz - numerical descriptions of data\n10 points possible answered: 3/11\nquestion 4\na sample of…

Explanation:

Step1: Calculate the mean

$\bar{x}=\frac{14 + 2+1+19+15}{5}=\frac{51}{5}=10.2$

Step2: Calculate the squared - differences

$(14 - 10.2)^2=3.8^2 = 14.44$ $(2 - 10.2)^2=(-8.2)^2 = 67.24$ $(1 - 10.2)^2=(-9.2)^2 = 84.64$ $(19 - 10.2)^2=8.8^2 = 77.44$ $(15 - 10.2)^2=4.8^2 = 23.04$

Step3: Calculate the sum of squared - differences

$S=\ 14.44+67.24 + 84.64+77.44+23.04=266.8$

Step4: Calculate the sample variance

$s^2=\frac{S}{n - 1}=\frac{266.8}{5 - 1}=\frac{266.8}{4}=66.7$

Step5: Calculate the sample standard deviation

$s=\sqrt{66.7}\approx8.2$

Answer:

$8.2$