To solve this problem one must be aware of the concepts of standard deviation and variance of raw data.
There is a direct formulae to calculate the variance of the data,
Variance = [tex]σ^{2} =\frac{Sigma(xi-m)^{2}}{n}[/tex]
Now here we need to verify ∑x and ∑[tex]x^{2}[/tex].
∑x = 21+19+15+32+27
= 114
and ∑[tex]x^{2}[/tex] = [tex]21^{2} +19^{2} +15^{2} +32^{2} +27^{2}[/tex]
= 441+361+225+1024+729
= 2780
So, the given relation is true.
Now the variance of the given data by putting the values in the formulae is equal to 45.2.
And Standard deviation=[tex]\sqrt{Variance}[/tex]
= [tex]\sqrt{45.2}[/tex]
= 6.72
And for population α²=36.16 and deviation=6.01.
To learn more about the deviation and variance visit the link:
https://brainly.com/question/16555520
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