Question

a sample was done, collecting the data below. calculate the standard deviation, to one decimal place.
|x|
|6|
|15|
|4|
|25|
|27|

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{6 + 15+4+25+27}{5}=\frac{77}{5}=15.4$

Step2: Calculate the squared - differences

$(6 - 15.4)^2=(-9.4)^2 = 88.36$
$(15 - 15.4)^2=(-0.4)^2 = 0.16$
$(4 - 15.4)^2=(-11.4)^2 = 129.96$
$(25 - 15.4)^2=(9.6)^2 = 92.16$
$(27 - 15.4)^2=(11.6)^2 = 134.56$

Step3: Calculate the variance

The variance $s^2=\frac{88.36+0.16 + 129.96+92.16+134.56}{5 - 1}=\frac{445.2}{4}=111.3$

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{111.3}\approx10.5$

Answer:

$10.5$