Mean, median, mode, variance, and other descriptive statistics measures and how each is calculated. Front: the term or formula. Back: definition or formula with a brief usage note.
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- Mean
- Sum of all values divided by the number of values; the arithmetic average.
- Median
- The middle value when data is ordered; the 50th percentile.
- Mode
- The most frequently occurring value in a dataset.
- Weighted mean
- Sum of each value multiplied by its weight, divided by the sum of weights; used when values have different importance.
- Geometric mean
- The nth root of the product of n values; useful for growth rates and investment returns.
- Range
- The difference between the largest and smallest values.
- Population variance
- The average of squared deviations from the population mean, denoted by sigma squared.
- Sample variance
- The sum of squared deviations from the sample mean divided by n-1; provides an unbiased estimate of population variance.
- Population standard deviation
- The square root of population variance; measures spread in the same units as the data.
- Sample standard deviation
- The square root of sample variance; estimates the population standard deviation with minimal bias.
- Coefficient of variation
- Standard deviation divided by the mean, often expressed as a percentage; allows comparison of spread across different scales.
- Interquartile range (IQR)
- The difference between the third quartile (Q3) and first quartile (Q1); contains the middle 50% of data.
- Mean absolute deviation
- The average of the absolute values of deviations from the mean; another measure of spread.
- Percentile
- A value below which a given percentage of observations fall; ranges from 0 to 100.
- Quartile
- Values that divide ordered data into four equal parts: Q1 (25th), Q2 (50th), Q3 (75th), Q4 (100th).