[VA] SRC#005- April, 1st Mean Minichallenge

[Valentin Albillo]

 
Hi all, welcome to my meaningless but well-meaning  SRC#005 - April, 1st  Mean Minichallenge.
      
Given a set of data consisting of positive real numbers  x₁, x₂, ..., x_n,  consider these four well-known means M_k for k = 1, 2, 3, 4:

      M₁ = the Harmonic Mean = \(\frac{n}{\frac{1}{x_1} + \frac{1}{x_2} + ... + \frac{1}{x_n}} \)

      M₂ = the Geometric Mean = \(\sqrt[n]{ x_1 x_2 ... x_n} \)

      M₃ = the Arithmetic Mean = \(\frac{x_1 + x_2 + ... + x_n}{n} \)

      M₄ = the Quadratic Mean = \(\sqrt{\frac{{x_1}^2 + {x_2}^2 + ... + {x_n}^2}{n}} \)

The Minichallenge:

Write code that accepts as input a dataset and the parameter k and returns the value of the corresponding mean M_k. For instance, for the sample dataset  4, 1, 20.19  your code should return:

      k = 1:   M₁ = 2.3085... (Harmonic mean)

      k = 2:   M₂ = 4.3224... (Geometric mean)

      k = 3:   M₃ = 8.3966... (Arithmetic mean)

      k = 4:   M₄ = 11.8972... (Quadratic mean)

Now, with the same sample dataset, use your code to return the values of the means  M_5/2 , M_Pi , M_-2.019  and  M_0.61. Also, find the value of k which makes  M_k = Pi.

In a day or so I'll post my original solution which is a 3-line (138 bytes) subprogram for the HP-71B, but in the meantime see what you can do with any HP calc (not Excel, Python, etc.) of your choice and please post both code and results, not just math expressions or text explanations and such. Enjoy !

V.