Mean, Median, Mode, Range Calculator
Calculate statistical measures including mean, median, mode, range, standard deviation, and variance for a set of numbers.
About Statistical Measures
Statistical measures help us understand and interpret data by providing different ways to summarize and analyze a set of values.
Mean (Average)
The mean is the sum of all values divided by the number of values. It represents the central tendency of the data.
Mean = (x₁ + x₂ + ... + xₙ) / n
Where:
x₁, x₂, ..., xₙ = individual data points
n = number of data points
Median
The median is the middle value when the data is arranged in order. If there is an even number of values, the median is the average of the two middle values.
For the data set: 3, 5, 7, 9, 11
The median is 7 (the middle value)
For the data set: 3, 5, 7, 9
The median is (5 + 7) / 2 = 6
Mode
The mode is the value that appears most frequently in the data set. A data set can have no mode, one mode, or multiple modes.
For the data set: 3, 5, 5, 7, 9, 9, 9, 11
The mode is 9 (appears three times)
Range
The range is the difference between the maximum and minimum values in the data set. It provides a measure of the spread or dispersion of the data.
Range = Maximum value - Minimum value
Standard Deviation
The standard deviation measures the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.
Standard Deviation = √(Variance)
Variance = Σ(xᵢ - μ)² / n
Where:
xᵢ = each value in the data set
μ = mean of the data set
n = number of values in the data set
Geometric Mean
The geometric mean is the nth root of the product of n numbers. It is useful for data sets with values that have different scales or when calculating average rates of change.
Geometric Mean = ⁿ√(x₁ × x₂ × ... × xₙ)
Applications of Statistical Measures
- Education: Analyzing test scores, grading on a curve
- Finance: Calculating average returns, risk assessment
- Science: Analyzing experimental data, identifying outliers
- Business: Quality control, market research, sales forecasting
- Sports: Player statistics, team performance analysis