A list of numbers hides its story until you summarize it. This calculator takes any comma-separated data set and returns the essentials at once: mean, median, standard deviation, sum, and count — the vocabulary of every data conversation.
यह कैसे काम करता है
The mean is the sum divided by the count. The median is the middle value after sorting (or the average of the two middle values). The standard deviation measures how far values typically sit from the mean.
सूत्र
μ is the mean, N the count; this is the population standard deviation. For a sample drawn from a larger population, statisticians divide by N − 1 instead, giving a slightly larger value.
हल किया उदाहरण
The set 2, 4, 4, 4, 5, 5, 7, 9: mean = 40 ÷ 8 = 5, median = 4.5, and the squared deviations sum to 32, so σ = √(32 ÷ 8) = 2.
सामान्य प्रश्न
When should I trust the median over the mean?
Whenever outliers or skew exist — incomes, house prices, response times. One billionaire in the room shifts the mean enormously but barely moves the median.
What does the standard deviation actually tell me?
Typical distance from the mean. For roughly bell-shaped data, about 68% of values fall within one σ of the mean and 95% within two — the basis of most quality-control limits.
Population vs sample standard deviation — which is this?
This calculator computes the population version (÷ N). If your data is a sample representing something larger, the sample version (÷ N−1) is the statistically correct estimator; for large N the difference is negligible.