the manager of an electrical supply store measured

Answered question

2022-04-01

the manager of an electrical supply store measured th diameters of the rolls of wire in the inventory. The diameter of the rolls are listed below 0.56,  0.622, 0.154, 0.412, 0.287, 0.118

Answer & Explanation

RizerMix

RizerMix

Expert2022-05-03Added 583 answers

First sort the numbers into ascending order (from least to greatest):
0.118, 0.154, 0.287, 0.412, 0.56

Now let's find the mean. So add up all of the numbers and divide the sum by the number of numbers

Mean=0.118+ 0.154+ 0.287+ 0.412+ 0.565=1.5315=0.3062

So the mean is 0.3062

Use this formula to find the Standard Deviation:
Standard Deviation: σ=1N-1i=0N(xi-x)2

where x is the average, xi is the ith number, and N is the number of numbers

So we can replace N with 5

15-1i=0N(xi-x)2

Subtract 5-1 to get 4

14i=0N(xi-x)2

Replace x with 0.3062
14i=0N(xi-0.3062)2

Expand the summation (replace each xi with the respective number)

14((0.118-0.3062)2+(0.154-0.3062)2+(0.287-0.3062)2+(0.412-0.3062)2+(0.56-0.3062)2)

14((-0.1882)2+(0.154-0.3062)2+(0.287-0.3062)2+(0.412-0.3062)2+(0.56-0.3062)2)

Raise -0.1882 to the power of 2.

14(0.03541924+(0.154-0.3062)2+(0.287-0.3062)2+(0.412-0.3062)2+(0.56-0.3062)2)

Subtract 0.3062 from 0.154.

14(0.03541924+(-0.1522)2+(0.287-0.3062)2+(0.412-0.3062)2+(0.56-0.3062)2)

Raise -0.1522 to the power of 2.

14(0.03541924+0.02316484+(0.287-0.3062)2+(0.412-0.3062)2+(0.56-0.3062)2)

Subtract 0.3062 from 0.287.

14(0.03541924+0.02316484+(-0.0192)2+(0.412-0.3062)2+(0.56-0.3062)2)

Raise -0.0192 to the power of 2.

14(0.03541924+0.02316484+0.00036864+(0.412-0.3062)2+(0.56-0.3062)2)

Subtract 0.3062 from 0.412.

14(0.03541924+0.02316484+0.00036864+0.10582+(0.56-0.3062)2)

Raise 0.1058 to the power of 2.

14(0.03541924+0.02316484+0.00036864+0.01119364+(0.56-0.3062)2)

Subtract 0.3062 from 0.56.

14(0.03541924+0.02316484+0.00036864+0.01119364+0.25382)

Raise 0.2538 to the power of 2.

14(0.03541924+0.02316484+0.00036864+0.01119364+0.06441444)

Add 0.03541924 and 0.02316484.

14(0.05858408+0.00036864+0.01119364+0.06441444)

Add 0.05858408 and 0.00036864.

14(0.05895272+0.01119364+0.06441444)

Add 0.05895272 and 0.01119364.

14(0.07014636+0.06441444)

Add 0.07014636 and 0.064414440.06441444.

140.1345608

Combine 14 and 0.1345608.

0.13456084

Divide 0.1345608 by 4.

0.0336402

The result can be shown in multiple forms.

Exact Form:

0.0336402

Decimal Form:

0.18341264

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