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Listed below are the top 10 annual salaries​ (in millions of​ dollars) of TV personalities. Find the​ range, variance, and standard deviation for the sample data. Given that these are the top 10​ salaries, do we know anything about the variation of salaries of TV personalities in​ general? 39 38 37 30 20 18 17 14 13.6 12.7

1 Answer

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Range is 26.3

Variance is 119.20

Standard deviation is 10.9

The higher values for range, variance, and standard deviation indicate a wide spread in the salary data.

What is variance?

Given

Dataset: 39 38 37 30 20 18 17 14 13.6 12.7

a) Range is the highest - the smallest

Range = 39 - 12.7 = 26.3.

b) variance = Σ(x - xbar)²/n-1

n = 10

xbar = mean

xbar = 39+38+37+30+20+18+17+14+13.6+12.7/10

= 239.3/10 = 23.93

Variance = (39-23.93)²+(38-23.93)²+(37-23.93)²+(30-23.93)²+(20-23.93)²+(18-23.93)²+(27-23.93)²+(14-23.93)²+(13.6-23.93)²+(12.7-23.93)²/10-1

= 227.105+197.965+170.825+36.845+15.445+35.165+48.025+98.605+106.709+126.113

= 1072.822/9 = 119.20

The variance of the data is 119.20

c) Standard deviation = √variance

S.D = √119.20 = 10.9

The consistent values for range, variance, and standard deviation in the provided top 10 TV personalities' salaries indicate significant variation, reflecting a wide spread in salaries of TV personalities.

User Fabio Carello
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