Question

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? 42       40       38       30       21       18       16       13       12.8       11.4 The range of the sample data is ​$nothing million. ​(Type an integer or a​ decimal.) The variance of the sample data is nothing . ​(Round to two decimal places as​ needed.) The standard deviation of the sample data is ​$nothing million. ​(Round to two decimal places as​ needed.) Is the standard deviation of the sample a good estimate of the variation of salaries of TV personalities in​ general?

Answer 1

Arrange the given data in ascending order

11.4
12.8
13
16
18
21
30
38
40
42

a)

Range = max - min
= 42 - 11.4
= 30.6

b)
first find the mean of the given data,
mean = sum/10 = 242.2/10 = 24.22
sum of squares = sum((x - xbar)^2) = ((11.4 - 24.22)^2 + (12.8 - 24.22)^2 + ....+ (11.4 - 24.22)^2 ) = 1325.716

Sample variance = sum of squares / (n -1)
variance = 1325.716/9 = 147.3018
= 147.30 (rounding to 2 decimal places)

x	(x-xbar)^2
11.4	164.3524
12.8	130.4164
13	125.8884
16	67.5684
18	38.6884
21	10.3684
30	33.4084
38	189.8884
40	249.0084
42	316.1284

c)
Sample standard deviation = sqrt(variance)
= sqrt(147.3018)
= 12.1368

= 12.14 (rounding to 2 decimal places)