This Question: 1 pt 7 of 16 (4 complete) This Test: 16 pts possible Listed below

Question

This Question: 1 pt 7 of 16 (4 complete) This Test: 16 pts possible Listed below are the gross amounts (in millions of dollars) earned in box office receipts for a recent movie. The amounts are listed in order for the first 14 days of the movies release. Find the range, variance, and standard deviation of the data set. If you invested in this movie, what characteristic of the data set would you care about most, and is it a measure of center or variation? 60 57 53 43 38 35 21 21 20 6 The range of the sample data ismillion dollars Round to one decimal place as needed.) The variance of the sample data is million dollars Round to one decimal place as needed.) The standard deviation of the sample data is million dollars. Round to one decimal place as needed.) If you invested in this movie, what characteristic of the data set would you care about most, and is it a measure of center or variation? A. The standard deviation, and it is a measure of variation. O B. The vanance, and it is a measure of variation. C. The variance, and it is a measure of center D. The standard deviation, and it is a measure of center E. The gross from opening day and the rate of decline. The measures of center and variation are less important.

Explanation / Answer

Here, n=number of observations =14

Data(xi):60 57 53 44 43 38 35 21 21 20 17 14 7 6

(a) Here, Maximum(xi)=60 & Minimum(xi)=6

Range=Maximum(xi)- Minimum(xi)=60-6=54

(b) Let us compute sample mean

x-=xi/n=436/14=31.14286

By defination , variance is ,

Variance=(xi-x-)2/(n-1)=(xi-31.14286)2/13=4385.714/13= 337.3626

(c) Standard deviation is,

Standard deviation=sqrt(Variance)=sqrt(337.3626)=18.36743

(d) Answer of this question is option A. & option B.

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