Answer to Question #262176 in Statistics and Probability for Aashish

Question #262176

How do I find the values of more than one data in a set given the values of harmonic geometric and arithmetic mean i.e


In a study a set of observations were as follows:x,16,20b,4,25,c.Given that the geometric mean is 8.433 the arithmetic mean 11.25 and the harmonic mean 6.026 compute the values x y z



1
Expert's answer
2021-11-15T19:27:09-0500
"x,20y, 4, 25, z"

"GM=\\sqrt[6]{x(16)(20y)(4)(25)(z)}=8.433"

"AM=\\dfrac{x+16+20y+4+25+z}{6}=11.25"

"HM=\\dfrac{6}{\\dfrac{1}{x}+\\dfrac{1}{16}+\\dfrac{1}{20y}+\\dfrac{1}{4}+\\dfrac{1}{25}+\\dfrac{1}{z}}=6.026"

"x(20y)z=224.787739"

"x+20y+z=22.5"

"\\dfrac{1}{x}+\\dfrac{1}{20y}+\\dfrac{1}{z}=0.643185"

"x+20y+z=22.5"

"x(20y)+x(z)+20y(z)=144.580101"



"x(20y)z=224.787739"

Vieta's Theorem


"t^3-22.5t^2+144.580101t-224.787739=0"

Solve graphically


"t_1=2.285, t_2=8.166, t_3=12.049"

Answer

"x=2.285, y=0.4083, z=12.049"

Or


"x=2.285, y=0.60245, z=8.166"

Or


"x=8.166, y=0.11425, z=12.049"

Or


"x=8.166, y=0.60245, z=2.285"

Or


"x=12.049, y=0.11425, z=8.166"

Or


"x=12.049, y=0.4083, z=2.285"


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