What Is a Statistics Calculator?
A statistics calculator computes descriptive statistics from a set of numbers — giving you a quick summary of what the data looks like. Rather than manually computing each measure, you paste in your numbers and instantly see key values: the average, the middle value, the most common value, how spread out the data is, and where the quartiles fall.
These measures are used everywhere: analysing test scores, understanding financial data, interpreting scientific results, and making sense of any numerical dataset.
How to Use This Statistics Calculator
Type or paste your numbers into the input box, separated by commas, spaces, or line breaks. The calculator updates in real time. Non-numeric entries (like letters or extra punctuation) are automatically ignored, and a warning shows how many values were skipped.
Formulas Used
Mean (Arithmetic Average)
Mean = Sum of all values ÷ Count
Example: [4, 8, 6, 5, 3, 2, 8, 9, 2, 5] → Sum = 52, Count = 10 → Mean = 5.2
Median
Sort the values. If N is odd, median = middle value. If N is even, median = average of the two middle values.
Example (even N): [2, 3, 4, 5, 5, 6, 8, 8, 9] sorted → middle values are 5 and 5 → Median = 5.0
Mode
The value(s) that appear most frequently. A dataset can have one mode (unimodal), two (bimodal), or more (multimodal). If all values are unique, there is no mode.
Standard Deviation
Population σ = √[ Sum(xᵢ − μ)² ÷ N ]
Sample s = √[ Sum(xᵢ − x̄)² ÷ (N−1) ]
Use population σ when you have all data; use sample s when your data is a subset of a larger population.
Quartiles (Q1, Q3) and IQR
Q1 is the median of the lower half of sorted data. Q3 is the median of the upper half. IQR = Q3 − Q1. The IQR represents the spread of the middle 50% of values and is resistant to outliers.
When to Use Each Statistic
- Mean: Best for symmetric, normally distributed data without outliers. Use for test averages, typical measurements.
- Median: Best when data has outliers or is skewed. Use for income data, house prices, response times.
- Mode: Best for categorical or discrete data. Use to find the most common value in a survey or count dataset.
- Std Dev: Measures spread. Use to compare variability between datasets or understand score distribution.
- IQR: Robust measure of spread. Use to detect outliers (Tukey fence: outlier if < Q1 − 1.5×IQR or > Q3 + 1.5×IQR).
Frequently Asked Questions
What is the difference between population and sample standard deviation?
Population std dev (σ) divides by N and applies when you have every data point in the population. Sample std dev (s) divides by N−1 (Bessel's correction) and applies when your data is a sample. In practice, use the sample version for most analysis and research.
What does standard deviation tell you?
Standard deviation tells you how spread out values are from the mean. A small std dev means values cluster tightly around the mean. A large std dev means values are spread widely. For example, exam scores of 78, 80, 82 (std dev ≈ 2) are tightly grouped, while scores of 40, 75, 95 (std dev ≈ 22.5) are widely spread.
What is the IQR and why does it matter?
The interquartile range (IQR = Q3 − Q1) spans the middle 50% of data. Unlike range (max − min), it is not affected by extreme outliers. It is used in box plots and for detecting outliers: any value more than 1.5×IQR beyond Q1 or Q3 is considered a potential outlier.
When is the median better than the mean?
When data is skewed or contains outliers. Income statistics use the median — a small number of very high earners would inflate the mean far above typical incomes. The median always represents the middle of the distribution regardless of extremes.
What does it mean if a dataset has no mode?
If every value appears exactly once, the data has no mode. If two or more values tie for highest frequency, the dataset is multimodal with multiple modes. For example, {1, 2, 2, 3, 3} has two modes: 2 and 3 (bimodal).