Question

find the sample standard deviation of the following set of four values. your answer should have two digits after the decimal place. make sure that you use the sample standard deviation and not the population standard deviation.
1.4
2.8
2.3
1.5

Explanation:

Step1: Calculate the mean

$\bar{x}=\frac{1.4 + 2.8+2.3 + 1.5}{4}=\frac{8}{4}=2$

Step2: Calculate squared - differences

$(1.4 - 2)^2=(-0.6)^2 = 0.36$
$(2.8 - 2)^2=(0.8)^2=0.64$
$(2.3 - 2)^2=(0.3)^2 = 0.09$
$(1.5 - 2)^2=(-0.5)^2=0.25$

Step3: Calculate the sum of squared - differences

$S=\ 0.36+0.64 + 0.09+0.25=1.34$

Step4: Calculate the sample variance

$s^2=\frac{S}{n - 1}=\frac{1.34}{4 - 1}=\frac{1.34}{3}\approx0.45$

Step5: Calculate the sample standard deviation

$s=\sqrt{s^2}=\sqrt{0.45}\approx0.67$

Answer:

$0.67$