The following data are the distances between 20 retail stores and a large distribution center. The distances are in miles. 29; 37; 38

Question

The following data are the distances between 20 retail stores and a large distribution center. The distances are in miles.
29; 37; 38; 40; 58; 67; 68; 69; 76; 86; 87; 95; 96; 96; 99; 106; 112; 127; 145; 150
Find the variance and standard deviation (round each to the nearest tent

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Thu Nguyệt 4 years 2021-08-11T11:38:24+00:00 1 Answers 6 views 0

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  1. mit
    0
    2021-08-11T11:39:34+00:00
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    Answer:

    1191.4 ; 34.5

    Step-by-step explanation:

    Given the data:

    29; 37; 38; 40; 58; 67; 68; 69; 76; 86; 87; 95; 96; 96; 99; 106; 112; 127; 145; 150

    The sample variance and standard deviation can be obtained thus :

    Σ(X – m)² / (n – 1)

    Where, m = mean of the sample

    n = sample size

    The standard deviation equals, sqrt(variance )

    Using a calculator:

    The variance, σ² ;

    Mean = Σx / n = 1681 / 20 = 84.05

    (x -m)^2

    [(29-84.05)^2 + (37-84.05)^2 + (38-84.05)^2 + (40-84.05)^2 + (58-84.05)^2 + (67-84.05)^2 + (68-84.05)^2 + (69-84.05)^2 + (76-84.05)^2 + (86-84.05)^2 + (87-84.05)^2 + (95-84.05)^2 + (96-84.05)^2 + (96-84.05)^2 + (99-84.05)^2 + (106-84.05)^2 + (112-84.05)^2 + (127-84.05)^2 + (145-84.05)^2 + (150-84.05)^2] / 19

    22636.95 / 19

    = 1191.4184 = 1191.42

    Standard deviation = sqrt( Variance)

    Standard deviation = sqrt(1191.4184)

    Standard deviation = 34.516929 = 34.52

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