Question

Given the sample data. x: 23 17 13 32 27 (a) Find the range. (b) Verify that Zr = 112 and Zr2 = 2,740. 2x= Zr2- (c) Use the results of part (b) and appropriate computation formulas to compute the sample variance s2 and sample standard deviation s. (Round your answers to two decimal places.) (d) Use the defining formulas to compute the sample variance s2 and sample standard deviation s. (Round your answers to two decimal places.) (e) Suppose the given data comprise the entire population of all x values. Compute the population variance σ2 and population standard deviation σ. (Round your answers to two decimal places.) σ=

Answer 1

a) range =max-min =32-13 =19

b)

x(x-x) 0.3600 29.1600 88.3600 92.1600 729.000 21.1600 2740 231.2000 22.400 s-2(x-X)'/(n-1)- 57.8000 7.603 23 17 13 32 27 112 529.000 289.000 169.000 1024.000

from above $\sum$x =112

and $\sum$x² =2740

c) s² =($\sum$x²-($\sum$x)²/n)/(n-1) =(2740-112²/5)/(5-1)=57.8

s =(57.8)^1/2 =7.60

d)from abvoe picture s² =($\sum$(x-xbar)²)/(n-1) =57.8

s =(57.8)^1/2 =7.60

e) $\sigma$² =($\sum$(x-xbar)²)/n =46.24

$\sigma$ =6.80