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

Answer:

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 .