Statistics Calculator

Calculate comprehensive statistical measures for your dataset including central tendency, dispersion, and z-scores.

What is Statistics?

Statistics is the science of collecting, analyzing, and interpreting data. Key statistical measures help us understand data distributions:

Measures of Central Tendency

These describe the center or typical value of a dataset:

• Mean: The arithmetic average of all values
• Median: The middle value when data is sorted
• Mode: The most frequently occurring value

Measures of Spread (Dispersion)

These describe how spread out the data is:

• Range: Difference between maximum and minimum values
• Variance: Average of squared differences from the mean
• Standard Deviation: Square root of variance, measures typical deviation
• Interquartile Range (IQR): Range of the middle 50% of data

Z-Score

The z-score indicates how many standard deviations a value is from the mean:

z = (x - μ) / σ

A z-score of 0 means the value equals the mean. Positive z-scores are above the mean, negative are below.

Applications of Statistics

Statistics is essential in many fields:

• Science: Experimental analysis and hypothesis testing
• Business: Market research and quality control
• Medicine: Clinical trials and epidemiology
• Social Sciences: Survey analysis and demographic studies
• Finance: Risk assessment and portfolio analysis