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? 41 39 38 31 21 20 18 16 15.7 15.2

a) Range = 25.8 million

Variance = 1008.129

Standard deviation = 10.04 million

b) No, we do not know anythjng about the variation of salaries of TV personalities in general as the behaviour of the entire data set cannot be determined just by examining the topmost values. For all we know, these could be the most outlier numbers.

Step-by-step explanation:

The top 10 annual salaries (in million of dollars) of TV personalities

41 39 38 31 21 20 18 16 15.7 15.2

Range = Difference between the highest value and the lowest value.

For this set of data,

Range = 41 - 15.2 = 25.8 million.

Variance is an average of the squared deviations from the mean.

It is given mathematically as

Variance = [Σ (x - xbar) ²/N]

where x = each variable

xbar = mean of the data set

N = number of variables = 10

First of, we find the mean,

The mean, xbar, is the sum of variables divided by the number of variables.

xbar = (Σx) / N = (41 + 39 + 38 + 31 + 21 + 20 + 18 + 16 + 15.7 + 15.2) / 10 = (254.9/10)

xbar = 25.49

Σ (x - xbar) ² = (41 - 25.49) ² + (39 - 25.49) ² + (38 - 25.49) ² + (31 - 25.49) ² + (21 - 25.49) ² + (20 - 25.49) ² + (18 - 25.49) ² + (16 - 25.49) ² + (15.7 - 25.49) ² + (15.2 - 25.49) ² = 1008.129

Variance = [Σ (x - xbar) ²/N] = (1008.129/10)

Variance = 100.8129

Standard deviation = √ (variance) = √ (100.8129) = 10.04 million