Statistical Tools

Calculate essential statistical measures including mean, median, mode, standard deviation, variance, and correlation. Perfect for data analysis, research, business analytics, and education.

Statistical Tools
Calculate essential statistical measures including mean, median, standard deviation, variance, and correlation

Quick Examples

Variance → Standard Deviation
Enter 16 in "Variance" and convert to "Standard Deviation" (√16 = 4)
Correlation → R²
Enter 0.8 in "Pearson Correlation" and convert to "Correlation Squared" (0.8² = 0.64)

Common Use Cases

  • Data Analysis: Calculate descriptive statistics for datasets
  • Research: Analyze experimental results and survey data
  • Business Analytics: Calculate performance metrics and trends
  • Education: Learn and practice statistical concepts
  • Quality Control: Monitor process variability and performance

Popular Calculations

Mean = 10Variance = 25
Variance = 16Std Dev = 4
r = 0.8R² = 0.64
Q1 = 25, Q3 = 75IQR = 50

How Our Statistical Tools Work

1️⃣

Enter Statistical Value

Input your statistical measure in the "From" field. Our tools accept decimal numbers, fractions, and mathematical expressions.

2️⃣

Select Calculation

Choose your source statistical measure and target measure from our comprehensive selection including central tendency, dispersion, and correlation.

3️⃣

Get Instant Result

View the calculated statistical measure in real-time. Copy results, explore common calculations, or check calculation history.

Understanding Statistical Measures

Central Tendency

Arithmetic Mean (x̄)
The sum of all values divided by the number of values. Most commonly used measure of central tendency.
Median (M)
The middle value when data is ordered. Robust to outliers and represents the 50th percentile.

Dispersion

Variance (σ²)
Average squared deviation from the mean. Measures the spread of data around the central value.
Standard Deviation (σ)
Square root of variance. Most commonly used measure of variability, in the same units as the data.

Percentiles

Quartiles (Q1, Q2, Q3)
Q1 (25th percentile), Q2 (50th percentile/median), Q3 (75th percentile). Divide data into four equal parts.
Interquartile Range (IQR)
Difference between Q3 and Q1. Robust measure of spread that is less sensitive to outliers than range.

Correlation

Pearson Correlation (r)
Linear correlation coefficient ranging from -1 to +1. Measures strength and direction of linear relationship.
Coefficient of Determination (R²)
Square of correlation coefficient. Represents the proportion of variance explained by the relationship.

Frequently Asked Questions

When should I use mean vs. median?

Use the mean when your data is normally distributed and has no significant outliers. Use the median when your data is skewed or contains outliers, as it's more robust and represents the typical value better in these cases.

What does a correlation coefficient tell us?

A correlation coefficient (r) ranges from -1 to +1. Values close to +1 indicate strong positive correlation, values close to -1 indicate strong negative correlation, and values close to 0 indicate no linear relationship.

How do I interpret standard deviation?

Standard deviation measures how spread out your data is from the mean. In a normal distribution, about 68% of data falls within ±1 standard deviation of the mean, 95% within ±2 standard deviations, and 99.7% within ±3 standard deviations.

What are percentiles used for?

Percentiles indicate the value below which a given percentage of observations fall. They're useful for understanding data distribution, identifying outliers, setting thresholds, and comparing individual values to the overall dataset.

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