Range Calculator

The range is the difference between the largest and smallest values in a data set. It gives an immediate picture of total spread and is easy to interpret in the original measurement units. A range of 8 means the highest observation is eight units above the lowest. Because it depends only on two observations, however, one extreme value can change it dramatically while every middle value stays the same. This calculator supplements the range with measures of center and dispersion. The arithmetic mean is the sum divided by the number of observations. The median is the middle value after sorting, or the average of the two middle values when the count is even. The mode lists the most frequent value or values; when every value appears once, the data have no mode. Each measure describes a different feature, so reporting several together gives a fuller summary. Population variance averages the squared distance from the mean across all entered values. Squaring prevents positive and negative deviations from canceling and gives extra weight to distant observations. Population standard deviation is the square root of that variance, which returns dispersion to the original units. Use these population formulas when the entered values are the entire group you want to describe. If they are a sample used to estimate a broader population, sample variance normally divides by n minus one instead. The mean and standard deviation work best as a pair for roughly symmetric data without severe outliers. The median and an interquartile measure are often more representative for skewed distributions. The mode is useful for repeated discrete values and categories represented numerically, while the range is valuable for checking operational limits or spotting a surprising extreme. No single statistic captures distribution shape. Enter negative values, decimals, or repeated observations using commas, spaces, or semicolons. Every occurrence contributes to the count, sum, mean, variance, and frequency calculation. Results are rounded to six decimal places for readability, but calculations retain ordinary floating-point precision. Before drawing conclusions, confirm that all values use the same units, that missing observations were handled consistently, and that the data set actually represents the population or sample described in your analysis.