Answer:
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.
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