Calculation: The arithmetic mean, often referred to as the average, is calculated by summing up all the values in a dataset and dividing the sum by the number of values.

Formula: Arithmetic Mean (A) = (X₁ + X₂ + … + Xₙ) / n o where X₁, X₂, …, Xₙ are the individual values in the dataset, and n is the number of values.

Nature: The arithmetic mean is sensitive to extreme values (outliers). A single unusually high or low value can significantly affect the mean.

Common Use: It is commonly used for simple averaging in everyday situations, such as calculating the average score in a class or the average temperature over a period. Geometric Mean:

Calculation: The geometric mean is calculated by multiplying all the values in a dataset and then taking the nth root, where n is the number of values.

Nature: The geometric mean is less sensitive to extreme values compared to the arithmetic mean. It is a useful measure for situations where the relative magnitudes of values are significant.

Common Use: It is often used in finance to calculate the average rate of return on an investment over multiple periods. Harmonic Mean:

Calculation: The harmonic mean is calculated by taking the reciprocal of the arithmetic mean of the reciprocals of the values in a dataset.

Formula: Harmonic Mean (H) = n / [(1/X₁) + (1/X₂) + … + (1/Xₙ)] here X₁, X₂, …, Xₙ are the individual values in the dataset, and n is the number of values.

Nature: The harmonic mean gives more weight to smaller values in the dataset. It is highly influenced by outliers, especially extremely small values.

Common Use: It is commonly used in situations where the emphasis is on rates or ratios, such as calculating average speeds or average rates of return.