print("hello world")
for i in range(100):
   print(i)

• hello
• hi

This document explains how to calculate the Arithmetic Mean (AM) for grouped frequency data.

$$ \text{Arithmetic Mean (AM)} = \frac{1}{N} \sum_{i=1}^{n} f_i x_i $$

Where:

• AM = Arithmetic Mean
• fᵢ = Frequency of the i-th class
• xᵢ = Mid-point (class mark) of the i-th class
• N = Total frequency (i.e., Σfᵢ)

Calculation:

AM = 240 / 10 = 24

The Geometric Mean (GM) is a measure of central tendency used when the data involves products or ratios, such as rates, percentages, growth factors, or logarithmic data.

The Geometric Mean of a set of n positive numbers is the nth root of their product:

GM = (x₁ × x₂ × x₃ × ... × xₙ)^(1/n)

Or more compactly:

GM = (∏ xᵢ)^(1/n)

Given values: x₁, x₂, ..., xₙ

1. Multiply all the values together:
   P = x₁ × x₂ × ... × xₙ

2. Take the nth root of the product:
   GM = P^(1/n)

1. Take the logarithm of each value:
   log(GM) = (1/n) × [log(x₁) + log(x₂) + ... + log(xₙ)]

2. Take the antilog to get GM:
   GM = antilog { (1/n) × Σ log(xᵢ) }

Given data: 4, 16, 64

Step 1: Multiply all the values:
4 × 16 × 64 = 4096

Step 2: Take the cube root (since n = 3):
GM = ³√4096 = 16

• Rates of change (e.g., growth rates, returns on investment)
• Percentages or indices
• Skewed distributions
• To avoid the influence of extreme values

Feel free to contribute examples or improvements via pull request.