Question

chapter 3 quiz - numerical descriptions of data
10 points possible answered: 3/11
question 4
a sample of data was collected below. calculate the sample standard deviation, to one decimal place.
|x|
|----|
|14|
|2|
|1|
|19|
|15|

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:

$8.2$