Types of Mean in Statistics

Mean in Statistics

It refers to a measure of central tendency, the typical or central value in a dataset. There are 5 several types, each suited to different data scenarios.

Types of Mean

1. Arithmetic Mean (AM):

• Definition: The sum of all values divided by the number of values.
• Use: General purpose average for quantitative data without extreme outliers.

2. Geometric Mean (GM):

• Definition: The nth root of the product of the values (where n is the number of values).
• Use: Growth rates, percentages, and multiplicative processes; sensitive to zero or negative values.

3. Harmonic Mean (HM):

• Definition: The reciprocal of the average of reciprocals; equivalently, n divided by the sum of reciprocals.
• Use: Rates or ratios, such as speeds or prices per unit; emphasizes smaller values.

4. Weighted Mean:

• Definition: Each value is multiplied by a weight, then the sum of these products is divided by the sum of the weights.
• Use: When observations have varying importance or frequency.

5. Other Notable Means:

i. Root Mean Square (RMS):

• Definition: Square root of the average of squares of the values.
• Use: Quantities that are squared before averaging, such as in signal processing.

ii. Contraharmonic Mean:

• Definition: The mean of squares divided by the mean; relates to areas where higher values are overweighted.
• Use: Some signal processing and image processing contexts.