StatsCore

Statistics Calculator

Paste any dataset (commas, spaces, or new lines) — get every descriptive statistic in one view.

Dataset (commas, spaces, or new lines)

Std. dev. type:

Count

Sum

127

Mean

12.7

Median

Min

Max

Range

Mode

12, 8

Variance

19.789

Std. deviation

4.449

Descriptive statistics for worked datasets

Mean, median, mode and both standard deviations for three datasets. Sample SD divides by n minus 1; population SD divides by n.

Dataset	Mean	Median	Mode	Sample SD	Population SD
12, 8, 15, 22, 8, 10, 17, 9, 12, 14	12.70	12.00	12/8	4.4485	4.2202
4, 8, 15, 16, 23, 42	18.00	15.50	none	13.4907	12.3153
2, 2, 3, 5, 7, 7, 7	4.71	5.00	7	2.3604	2.1853

The first dataset is bimodal - both 12 and 8 appear twice - which is worth knowing because software often reports only the first mode it finds and hides the second. The second row has no mode at all and shows the mean pulled to 18.00 by the outlying 42 while the median sits at 15.50, the classic signature of a right-skewed set. In the third the mean of 4.71 is below the median of 5.00, pulled down by the pair of 2s. Whenever mean and median disagree materially, the median is usually the better summary.

Sample vs. population

Use sample standard deviation (divide by n−1) when your data is a sample of a larger group. Use population (divide by n) when it represents the entire group.

Which average to use

Mean is best for symmetric data without outliers. Median is better when data is skewed or has outliers (income, house prices). Mode identifies the most common value — useful for categorical data. Report all three for a complete picture.

Frequently asked questions

What is the difference between mean, median, and mode?

Mean: sum of all values ÷ count (arithmetic average). Median: the middle value when sorted (or average of the two middle values). Mode: the most frequently occurring value. For [1, 2, 2, 3, 10]: mean = 3.6, median = 2, mode = 2. The outlier (10) pulls the mean up but doesn't affect the median.

What is standard deviation?

Standard deviation measures how spread out values are from the mean. Low SD = values clustered near the mean. High SD = values widely spread. Calculated as the square root of variance. In a normal distribution, ~68% of data falls within ±1 SD, ~95% within ±2 SD, and ~99.7% within ±3 SD of the mean.

When should I use sample vs population standard deviation?

Use population SD (÷ by n) when your data IS the entire population (all students in a class, all products in inventory). Use sample SD (÷ by n−1) when your data is a sample from a larger population (a survey of 100 customers out of 10,000). The n−1 correction (Bessel's) prevents underestimating the true population variability.