PublicSoftTools

Statistics Calculator

Paste or type any set of numbers to instantly calculate mean, median, mode, standard deviation, variance, quartiles, and more. Supports sample and population statistics. Runs entirely in your browser.

10 numbers detected

Count10
Sum68
Mean6.8
Median7
Mode7
Minimum2
Maximum13
Range11
Q1 (25th percentile)4
Q3 (75th percentile)8.5
IQR4.5
Sample Variance13.7333
Sample Std Dev (s)3.7059

How the Statistics Calculator Works

  1. 1Enter or paste your numbers separated by commas or new lines into the input box.
  2. 2Toggle between Sample (n−1 denominator) or Population (n denominator) for variance and standard deviation.
  3. 3View all 13 statistics instantly — count, sum, mean, median, mode, min, max, range, Q1, Q3, IQR, variance, and standard deviation.
  4. 4Edit the data at any time — results update live as you type.

What Each Statistic Measures

Central tendency: Mean (arithmetic average), Median (middle value), Mode (most frequent value). Spread: Range (max − min), Variance (average squared deviation), Standard Deviation (square root of variance — same unit as the data). Distribution shape: Q1 (25th percentile), Q3 (75th percentile), IQR (Q3 − Q1, middle 50% range).

Statistics Tips

Mean vs median for skewed data

In skewed distributions (salary data, house prices), the median is more representative. A few very large values pull the mean up without affecting the median.

Check for outliers with IQR

Values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR are outliers by the standard Tukey method. Outliers can distort mean and standard deviation significantly.

Sample vs population choice

If your data represents a random sample (e.g., 30 students from a school of 1000), use sample mode. If it IS the entire group being analyzed, use population mode.

Copy data from spreadsheets

Copy a column of numbers from Excel or Google Sheets and paste directly — the calculator handles newline-separated data automatically.

Mode may not exist

If all values appear exactly once, there is no mode. The calculator reports "None" in this case. Multiple modes (bimodal data) are all listed.

Small sample caution

With fewer than 5–10 data points, standard deviation and quartiles are unreliable estimates of the population. Collect more data before drawing conclusions.

Frequently Asked Questions

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

Mean is the arithmetic average — sum all values and divide by count. Median is the middle value when sorted — not affected by extreme outliers. Mode is the most frequently occurring value. For skewed data (like income), median is usually more representative than mean. For symmetric distributions, mean and median are close.

When should I use sample vs population standard deviation?

Use population standard deviation (σ, divides by n) when your data IS the entire population. Use sample standard deviation (s, divides by n−1) when your data is a sample drawn from a larger population — the n−1 (Bessel's correction) compensates for underestimating the true population spread from a sample.

What is the IQR and why is it useful?

The IQR (Interquartile Range) is Q3 − Q1 — the range of the middle 50% of your data. It is resistant to outliers because it ignores the highest and lowest 25% of values. IQR is commonly used in box plots and to detect outliers: values more than 1.5 × IQR beyond Q1 or Q3 are typically flagged as outliers.

How do I enter data into the calculator?

Type or paste numbers separated by commas (e.g., 4, 7, 13, 2, 7) or press Enter between values. The calculator accepts any combination of spaces, commas, and new lines as separators. Decimals and negative numbers are supported.

What is variance and how does it relate to standard deviation?

Variance is the average of squared differences from the mean. Standard deviation is the square root of variance — bringing it back to the same unit as your data. Standard deviation is more interpretable (e.g., "scores vary by ±12 points") while variance is used in mathematical formulas like ANOVA.

How are Q1 and Q3 quartiles calculated?

The calculator uses linear interpolation (the same method as Excel's PERCENTILE function): Q1 is the 25th percentile and Q3 is the 75th percentile of the sorted dataset. For small datasets, different textbooks use slightly different methods, so results may differ from manual calculations by a small amount.