Variance and Standard Deviation Homework

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Drake University *

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011

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Industrial Engineering

Date

Dec 6, 2023

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docx

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2

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Variance and Standard Deviation Method 1 Method 2 Standard Dev. S 2 = ∑ ( X − X ) 2 N S 2 = ∑ X 2 − ( ∑ X ) 2 N N S = √ S 2 Problem 1 (will complete in lab) Simple frequency distribution of number of COVID cases per household for 5 households: Cases Deviation Squared Deviation 1 -2.2 4.84 3 -0.2 0.04 4 -0.8 0.64 3 -0.2 0.04 5 1.8 3.24 Compute the mean: 3.2 Compute the variance: 1.76 Compute the standard deviation: 1.32 Why do you need to square the deviations from the mean? To cancel out the negative values 1 = 0 = 8
Problem 2 (will complete in lab) Tests x f F(x) X 2 F(x 2 ) (x-x) (x-x)^2 f(x-x)^2 30-32 31 2 62 961 1922 13.252 175.616 351.231 27-29 28 6 168 784 4704 10.252 105.104 630.624 24-26 25 11 275 625 6875 7.252 52.592 578.512 21-23 22 21 462 484 10164 4.252 18.080 379.680 18-20 19 26 494 361 9386 1.252 1.568 40.755 15-17 16 18 288 256 4608 -1.748 3.056 54.999 12-14 13 13 169 169 2197 -4.748 22.887 293.065 6 9-11 10 7 70 100 700 -7.748 60.032 420.221 6-8 7 5 35 49 245 -10.748 115.520 577.598 3-5 4 4 16 16 64 -13.748 189.008 756.030 0 0-2 1 2 2 1 2 -16.748 280.496 560.991 Compute the Mean: 2041/115= 17.75 Compute the Variance (practice both formulas): 40.38 Compute the Standard Deviation: 6.35 2 = 4,643.71 = 40,867 = 2,041
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