Question

Identify Arithmetic Mean, Geometric Mean and Harmonic Mean from the following averages:
56.4, 59.8 and 55.8

Answer 1

Solution:-

Arithmetic Mean -

Arithmetic mean = Sum of all observations/Total number of observation
= (56.4 + 59.8 + 55.8)/3
= 172/3
Arithmetic Mean = 57.33

Geometric Mean -

       x                         Log x
    56.4                     1.7513
    59.8                     1.7767
    55.8                     1.7466
_________________________
   N = 3        ∑ logx = 5.2746
_________________________

G.M. = Antilog [∑ logx/N]
= Antilog [5.2746/3]
= Antilog 1.7582
Geometric Mean = 57.31

Harmonic Mean -

          x                               1/x
       56.4                           0.0177
       59.8                           0.0167
       55.8                           0.0179
_____________________________
      N = 3            ∑(1/x) = 0.0523
_____________________________

H.M. = N/∑(1/x)
= 3/0.523
Harmonic Mean = 57.36

Answer.