Statistics Calculator
Get the mean, median, mode, range, variance, standard deviation, and quartiles of a data set in one step, with the working shown.
كيفية استخدام هذه الحاسبة
- 1Paste or type your numbers, separated by commas, spaces, or new lines.
- 2Choose whether the data is a sample or the whole population.
- 3Read the full summary — centre, spread, and quartiles all at once.
طريقة الحساب
Descriptive statistics
mean = sum ÷ count median = middle value of the sorted data mode = most frequent value(s) variance = Σ(x − mean)² ÷ (n − 1 for a sample, n for a population) standard deviation = √variance
Descriptive statistics summarise a data set in three ways: where its centre lies, how spread out it is, and its shape. The mean, median, and mode describe the centre from different angles; the range, variance, and standard deviation describe the spread; and the quartiles describe how the data divides. Together they turn a list of numbers into a handful of figures that capture what the list is like.
مثال محلول
For 12, 15, 15, 18, 22, 25, 30: the mean is 19.57, the median (middle value) is 18, and the mode is 15 (it appears twice). The range is 30 − 12 = 18, and the sample standard deviation is about 6.35.
Statistics Calculator: الدليل الكامل
Mean, median, and mode — three kinds of average
The three 'averages' answer different questions and disagree in revealing ways. The mean is the arithmetic average, sensitive to every value including outliers. The median is the middle value when sorted, ignoring how extreme the outliers are. The mode is the most common value, the only average that works for categories as well as numbers.
The gap between them tells you about the data's shape. When mean and median are close, the data is roughly symmetric. When the mean is pulled well above the median, a few large values are stretching it — which is exactly why average income (mean) is far higher than typical income (median): a handful of very high earners drag the mean up while leaving the median where most people actually are.
Spread, and why n−1
Knowing the centre is not enough — two data sets with the same mean can look completely different if one is tightly clustered and the other wildly scattered. Standard deviation measures that spread as the typical distance of values from the mean. A small standard deviation means the data huddles near the average; a large one means it ranges widely.
The subtle point is the divisor. For a whole population you divide the squared deviations by n. For a sample — a subset used to estimate a larger group — you divide by n−1 instead, Bessel's correction. This is because a sample tends to underestimate the true spread (the sample mean sits closer to its own points than the real mean would), and dividing by the smaller n−1 nudges the estimate up to compensate. Pick 'sample' unless you genuinely have every member of the group.
Quartiles and the five-number summary
Quartiles split sorted data into four equal parts. The first quartile (Q1) is the value a quarter of the way through, the third (Q3) three-quarters through, and the median is the second quartile. Together with the minimum and maximum they form the five-number summary, which is what a box plot draws.
The interquartile range — Q3 minus Q1 — is a robust measure of spread that, unlike the standard deviation, is barely affected by extreme outliers, because it only looks at the middle half of the data. It is also the basis of the common outlier rule: values more than 1.5 times the IQR beyond Q1 or Q3 are flagged as unusual. This makes quartiles especially useful for messy real-world data where a few wild values would distort the mean and standard deviation.
الأسئلة الشائعة
What is the difference between mean, median, and mode?
The mean is the sum divided by the count. The median is the middle value when sorted. The mode is the most frequent value. They agree for symmetric data but diverge when outliers are present — the mean chases outliers while the median resists them.
Should I use sample or population standard deviation?
Use sample (dividing by n−1) when your data is a subset used to estimate a larger group — which is almost always. Use population (dividing by n) only when you have measured every member of the group. Sample is the safer default and the one most software uses.
What does standard deviation tell me?
It measures how spread out the data is — the typical distance of values from the mean. A small standard deviation means values cluster near the average; a large one means they scatter widely. Two data sets can share a mean yet have very different standard deviations.
Why is average income higher than typical income?
Because the mean is pulled up by a small number of very high earners, while the median — the middle person — is unaffected by how extreme the top is. Whenever a distribution has a long tail, the mean sits above the median, which is why the median is often the fairer 'typical' figure.