Given the sample data.<?xml:namespace prefix = o ns = \"urn:schemas-microsoft-co

Question

Given the sample data.<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

(a) Find the range.  =


(b) Verify that ?x = 123 and ?x2 = 3143.

(c) Use the results of part (b) and appropriate computation formulas to compute the sample variance s2 and sample standard deviation s. (Enter your answers to one decimal place.)

(d) Use the defining formulas to compute the sample variance s2 and sample standard deviation s. (Enter your answers to one decimal place.)

(e) Suppose the given data comprise the entire population of all x values. Compute the population variance ?2 and population standard deviation ?. (Enter your answers to one decimal place.)

Explanation / Answer

a) Range = Max - Min = 28-17= 11

b) sum(x) = 17+31+25+28+22=123

sum(x^2)=289+961+625+784+484= 3143

c) population variance = sum(x^2)/n - (sum(x)/n)^2 = 3143/5 - (123/5)^2 = 628.6 - 605.16 ~= 23.4

sample var = Pop. var * n/(n-1) = 23.4 * 5/4 ~= 29.3

sample std = sqrt (sam. var) ~= 5.4

d)

sample var. = sum((x-mean(x))^2)/(n-1)

mean(x) = sum(x)/n = 123/5 = 24.6

=> sample. var. = (7.4^2 + 6.4^2 + 0.4^2 + 3.4^2 + (-2.6)^2)/4 = 28.5

sample. std = sqrt(sam. var) ~= 5.3

e) pop. var = 23.4       ( from c )

pop. std = sqrt(pop. var) = 4.837

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