Question

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

Answer 1

Range = 29

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

Standard Deviation= √variance= √97.3= 9.864

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 .