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Statistics Calculator

Free online statistics calculator that automatically computes mean, variance, and standard deviation from your data. Useful tool for students, researchers, and data analysts.

Enter Data

How to Use

1. Enter Data: Input numbers separated by comma, space, or newline.

2. Calculate: Click the button to automatically compute statistics.

3. View Results: Check the calculated statistics and copy values as needed.

Statistical Measures Explained

Mean: Mean: The sum of all values divided by the number of values
Median: Median: The middle value when data is sorted in order
Mode: Mode: The most frequently occurring value in the data
Variance & Standard Deviation: Variance: A measure of how spread out the data is from the mean
Population Variance: Population variance/std dev: Calculated for entire population (divide by n)
Sample Variance: Sample variance/std dev: Calculated for sample data (divide by n-1)

Use Cases

Students: Grade analysis, test score statistics
Researchers: Experimental data analysis, statistical testing
Data Analysis: Understanding data distribution, outlier detection
Business: Sales analysis, KPI monitoring

※ Notice

Use population variance for entire population data, sample variance for sample data.
Generally, sample variance and sample standard deviation are used for sample data.
All calculations are performed in your browser and not sent to any server.

자주 묻는 질문 (FAQ)

평균, 중앙값, 최빈값의 차이는 무엇인가요?

평균(Mean)은 모든 데이터의 합을 개수로 나눈 값으로 가장 흔히 사용됩니다. 중앙값(Median)은 데이터를 크기 순으로 정렬했을 때 가운데 위치한 값으로, 극단적인 이상치의 영향을 덜 받습니다. 최빈값(Mode)은 가장 자주 등장하는 값으로, 카테고리형 데이터 분석에 특히 유용합니다.

표준편차란 무엇이고 어떻게 해석하나요?

표준편차는 데이터 값들이 평균으로부터 얼마나 퍼져 있는지를 나타내는 지표입니다. 표준편차가 클수록 데이터가 평균에서 멀리 분산되어 있고, 작을수록 평균 주변에 모여 있습니다. 예를 들어 시험 점수의 표준편차가 크면 학생들 간의 점수 격차가 크다는 것을 의미합니다.

모분산과 표본분산은 언제 각각 사용하나요?

모분산은 전체 모집단의 데이터를 모두 가지고 있을 때 사용하며, 데이터 개수(n)로 나눕니다. 표본분산은 모집단에서 일부만 샘플링한 경우 사용하며, n-1로 나누어 편향을 보정합니다. 실제 연구에서는 대부분 표본 데이터를 다루므로 표본분산과 표본표준편차를 더 자주 사용합니다.

사분위수(Quartile)란 무엇인가요?

사분위수는 데이터를 크기순으로 정렬하여 4등분하는 값입니다. 제1사분위수(Q1)는 하위 25%, 제2사분위수(Q2)는 중앙값(50%), 제3사분위수(Q3)는 상위 25% 위치의 값입니다. 사분위수 범위(IQR = Q3 - Q1)는 이상치 탐지와 데이터 분포 파악에 자주 활용됩니다.

Complete Guide to Basic Statistics

An easy-to-understand explanation of statistical concepts essential for understanding and analyzing data.

Understanding and Applying Descriptive Statistics

Descriptive statistics is a method of summarizing and expressing the characteristics of data. Mean, median, and mode represent the central tendency of data, while variance and standard deviation represent data dispersion. Both aspects must be understood together to correctly interpret data. For example, two companies with the same average salary can have completely different wage structures if their standard deviations differ. A company with a small standard deviation has similar salaries across employees, while a large standard deviation indicates a wide gap between high and low earners. This is why correct interpretation of statistical measures matters.

Fields Where Statistics Are Applied

In education, statistics are used to understand student grade distributions and learning levels. In healthcare, they are essential for analyzing clinical trial results and verifying treatment effectiveness. In business, statistics serve as a core decision-making tool for sales trend analysis, quality control, and customer satisfaction surveys. In sports, statistics are widely used to analyze player performance and develop strategies. From weather forecasting and election prediction to financial risk analysis, data-driven statistical analysis is conducted across virtually every field of modern society.

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