Question

a sample was done, collecting the data below. calculate the standard deviation, to one decimal place.

x
26
22
27
24
5

this is not a decimal or integer value.
enter an integer or decimal number more...

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{26 + 22+27+24 + 5}{5}=\frac{104}{5}=20.8$

Step2: Calculate the squared differences

$(26 - 20.8)^2=(5.2)^2 = 27.04$
$(22-20.8)^2=(1.2)^2=1.44$
$(27 - 20.8)^2=(6.2)^2=38.44$
$(24-20.8)^2=(3.2)^2 = 10.24$
$(5 - 20.8)^2=(-15.8)^2=249.64$

Step3: Calculate the variance

The variance $s^{2}=\frac{27.04+1.44 + 38.44+10.24+249.64}{5 - 1}=\frac{326.8}{4}=81.7$

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{81.7}\approx9.0$

Answer:

$9.0$