Question

Compute AM, GM and HM for 6, 8, 12, 36​

Answer 1

Step-by-step explanation:

there is a relation between AM , GM , and HM

GM^2 = √AM×HM

Answer 2

Answer:

AM = 15.5, GM = √12.4, HM = 9.9310

Step-by-step explanation:

There are two numbers 'a' and 'b'

then AM = a+b/2

HM = $\frac{2}{\frac{1}{a}+\frac{1}{b} } = \frac{2ab}{a+b}$

GM = ab

AM×HM = GM²

Given numbers are

6, 8, 12, 36

Arithmetic mean (AM) = $\frac{6+8+12+36}{4}$ = $\frac{62}{4}$ = 15.5

Harmonic mean (HM)  = $\frac{4}{\frac{1}{6}+\frac{1}{8} +\frac{1}{12} +\frac{1}{36} }$

       =$(\frac{4}{1})(\frac{72}{12+9+6+2}) = \frac{(4)(72)}{29} =9.9310$

Geometric mean (GM)² = AM × HM

                                      = √AM ×HM

                                     =√AM ×√HM

                                    = √15.5 ×√9.9310

                                    =√12.40

Therefore, AM = 15.5, GM = √12.4, HM = 9.9310