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19 May, 17:00

Listed below are the numbers of manatee deaths caused each year by collisions with watercraft. The data are listed in order for each year of the past decade.

(a) Find the range, variance, and standard deviation of the data set.

(b) What important feature of the data is not revealed through the different measures of variation?

80 68 71 72 95 89 97 72 75 81

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  1. 19 May, 17:22
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    Range = 29

    Variance = (X₁ - U) ² / N = 973/10 = 97.3

    Standard Deviation = √variance = √97.3 = 9.864

    Step-by-step explanation:

    Range = Difference between the highest and lowest value = 97-68 = 29

    Variance

    X₁ X₁-U (X₁ - U) ²

    80 0 zero

    68 - 12 144

    71 - 9 81

    72 - 8 64

    95 15 225

    89 9 81

    97 17 289

    72 - 8 64

    75 - 5 25

    81 1 1

    ∑ 800 ZERO 973

    u = ∑X₁ / 10=800/10=80

    Variance = (X₁ - U) ² / N = 973/10 = 97.3

    Standard Deviation = √variance = √97.3 = 9.864

    (b) The important feature of the data is not revealed through the different measures of variation is that the variability of two or more than two sets of data cannot be compared unless a relative measure of dispersion is used.
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