Statistics Calculator - Free Online Descriptive Statistics Tool
Statistics Calculator
Separate numbers with commas, spaces, or new lines. Minimum 2 numbers required.
Enter your data and click "Calculate Statistics" to see comprehensive analysis
Understanding Descriptive Statistics
Central Tendency Measures
Mean (Average)
Sum of all values divided by count. Sensitive to outliers.
Median
Middle value when data is sorted. Robust to outliers.
Mode
Most frequently occurring value in the dataset.
Variability Measures
Standard Deviation
Average distance from the mean. Shows data spread.
Variance
Average of squared deviations from mean.
Range & IQR
Range = Max - Min. IQR = Q3 - Q1 (middle 50%).
Distribution Shape
- •Skewness: Measures asymmetry (left/right tail)
- •Kurtosis: Measures tail heaviness vs normal
- •Normality: How close to bell curve shape
- •Outliers: Values far from typical range
Quartiles & Percentiles
Min ── Q1 ── Median ── Q3 ── Max
0% 25% 50% 75% 100%
Q1: 25% of data below this value
Q2: Median (50% below)
Q3: 75% of data below this value
IQR: Q3 - Q1 (middle 50% spread)
Frequently Asked Questions
What is the difference between mean, median, and mode?
Mean is the arithmetic average of all values. Median is the middle value when data is sorted. Mode is the most frequently occurring value. Mean is sensitive to outliers, median is robust to outliers, and mode shows the most common value in the dataset.
How do you calculate standard deviation?
Standard deviation measures how spread out data points are from the mean. Calculate it by: 1) Find the mean, 2) Calculate squared differences from mean, 3) Find average of squared differences (variance), 4) Take square root of variance. Formula: σ = √(Σ(x-μ)²/N)
What are quartiles and how are they used?
Quartiles divide data into four equal parts. Q1 (25th percentile) is the median of the lower half, Q2 (50th percentile) is the overall median, Q3 (75th percentile) is the median of the upper half. The Interquartile Range (IQR = Q3-Q1) measures spread and helps identify outliers.
How does the calculator detect outliers?
The calculator uses the IQR (Interquartile Range) method to detect outliers. Values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR are considered outliers. This is a robust method that works well for most distributions and is commonly used in box plots.
What do skewness and kurtosis measure?
Skewness measures the asymmetry of the distribution. Positive skewness indicates a right tail, negative indicates a left tail. Kurtosis measures the 'tailedness' - how much data is in the tails vs. center. High kurtosis means more outliers, low kurtosis means fewer outliers than a normal distribution.
When should I use descriptive vs. inferential statistics?
Descriptive statistics (mean, median, standard deviation) summarize and describe your current dataset. Use them to understand your data's characteristics. Inferential statistics help make predictions or generalizations about a larger population based on your sample data.
What sample size do I need for reliable statistics?
For basic descriptive statistics, even small samples (n≥5) can be meaningful. For reliable estimates and normal distribution assumptions, n≥30 is often recommended. Larger samples (n≥100) provide more stable estimates and better power for statistical tests.
How do I interpret the coefficient of variation?
Coefficient of Variation (CV) = (Standard Deviation / Mean) × 100%. It measures relative variability. CV < 15% indicates low variability, 15-35% is moderate, >35% is high variability. Use CV to compare variability between datasets with different units or scales.