Question

Consider the following sample data: 41 49 28 51 37 47 a. Calculate the range. b. Calculate MAD. (Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) c. Calculate the sample variance. (Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) d. Calculate the sample standard deviation. (Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

Answer 1

Sample = 41 49 28 51 37 47

a) Range = Maximum - Minimum = 51 - 28 = 23

b) Mean, $\bar x = \Sigma x/n = 253/6= 42.1667$

x	$|x-\bar x|$
41	1.1667
49	6.8333
28	14.1667
51	8.8333
37	5.1667
47	4.8333

$MAD = \frac{\Sigma|x-\bar x|}{n} = \frac{41}{6} = \textbf{6.83}$

c) Sample Variance, $\sigma^2$ =

$\inline = \frac{(41-42.1667)^2+(49-42.1667)^2+(28-42.1667)^2+(51-42.1667)^2+(37-42.1667)^2+(47-42.1667)^2}{6-1}$

$\inline = \textbf{75.37}$

d) Sample Standard deviation, $\inline \sigma = \sqrt{75.37} = \textbf{8.68}$