Calculadora de Estadísticas
Media, mediana, moda, desviación estándar y más — todo de una vez
Statistics Calculator
Calculate mean, median, mode, and standard deviation
Enter comma-separated numbers
Mean = sum / n, StdDev = sqrt(sum((xi - mean)^2) / n)What is a Statistics Calculator?
A Statistics Calculator is a math tool that analyzes a set of numbers and computes common statistical measures such as mean (average), median, mode, range, and often variance and standard deviation. These measures help summarize data so you can understand patterns, compare groups, and make decisions based on numbers.
Statistics is used in school assignments, business reporting, scientific research, finance, sports analytics, and everyday life (like tracking budgets or comparing test scores). Instead of manually calculating multiple values—especially for larger datasets—a statistics calculator gives results instantly and reduces mistakes.
This calculator is helpful whenever you have a list of values and want quick insights about the center of the data (typical value), the spread (how scattered values are), and whether there are values that stand out from the rest.
How to Use This Statistics Calculator
- Enter your data values -- Input numbers into the data field (numbers only)
- Separate values correctly -- Use commas, spaces, or new lines—depending on the calculator’s input format
- Click 'Calculate' -- to analyze the dataset
- Review the results -- such as mean, median, mode, range, and standard deviation (if shown)
- Adjust your list -- add or remove values and recalculate to compare different datasets
Tips:
- Make sure you don’t include extra symbols (like $ or %) unless the calculator supports them
- If your dataset contains decimals, enter them exactly (example: 12.5)
- If the calculator offers a choice between population vs sample statistics, pick the one that matches your situation (explained below)
Statistics Formulas
Let your dataset be: x₁, x₂, x₃, …, xₙ where n is the number of values.
Mean (Average)
Mean = (x₁ + x₂ + … + xₙ) / n
Sum all values, then divide by the count
Median
The middle value after sorting the numbers:
- If n is odd: median is the middle value
- If n is even: median is the average of the two middle values
Mode
The most frequently occurring value(s):
- Unimodal (one mode), bimodal (two), or multimodal
- No mode if all values occur equally often
Range
Range = max − min
The difference between the largest and smallest values
Variance and Standard Deviation
Variance measures spread by looking at how far values are from the mean.
Population formulas
- σ² = [ Σ(xᵢ − μ)² ] / n
- σ = √σ²
μ = population mean
Sample formulas
- s² = [ Σ(xᵢ − x̄)² ] / (n − 1)
- s = √s²
x̄ = sample mean
Example Calculations
Example 1: Mean, Median, Mode
Data: 2, 4, 4, 7, 9
Mean: (2 + 4 + 4 + 7 + 9) / 5 = 26 / 5 = 5.2
Median: sorted list is 2, 4, 4, 7, 9 → middle value is 4
Mode: 4 occurs most often → mode = 4
Results: Mean = 5.2, Median = 4, Mode = 4
Example 2: Range
Data: 12, 15, 19, 22, 30
Max: 30, Min: 12
Range: 30 − 12 = 18
Result: Range = 18
Example 3: Population Standard Deviation
Data: 1, 2, 3
Mean (μ): (1 + 2 + 3) / 3 = 2
Differences: (1−2) = −1, (2−2) = 0, (3−2) = 1
Squared → Sum: 1 + 0 + 1 = 2
σ²: 2 / 3 = 0.6667
σ: √0.6667 ≈ 0.8165
Result: Population SD ≈ 0.8165
Example 4: Sample Standard Deviation
Data: 1, 2, 3
Mean (x̄): 2
Squared differences sum: 2 (same as above)
s²: 2 / (3 − 1) = 2 / 2 = 1
s: √1 = 1
Result: Sample SD = 1
Frequently Asked Questions
What’s the difference between mean, median, and mode?
The mean is the average (sum divided by count). The median is the middle value when sorted. The mode is the most frequent value. They can differ, especially if the data has outliers.
What are outliers, and how do they affect statistics?
Outliers are values far from the rest of the data. They can strongly affect the mean and standard deviation, but the median is usually more resistant to outliers.
What’s the difference between population and sample standard deviation?
Use population formulas when your dataset includes every member of the group you’re studying. Use sample formulas when your dataset is a subset (sample) of a larger population. Sample formulas divide by (n − 1) to reduce bias.
Can a dataset have more than one mode?
Yes. If two values tie for most frequent, it’s bimodal. If more than two values tie, it’s multimodal. If all values occur equally often, it may have no mode.
Why is standard deviation useful?
Standard deviation shows how spread out the data is. A low standard deviation means values are close to the mean; a high standard deviation means values vary widely.
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¿Qué son las estadísticas descriptivas?
La estadística es la ciencia de recopilar, analizar e interpretar datos numéricos. Las estadísticas descriptivas resumen las características clave de un conjunto de datos: tendencia central (media, mediana, moda) y dispersión (rango, varianza, desviación estándar). En lugar de sacar conclusiones sobre una población mayor, simplemente describen lo que contienen tus datos.
Las estadísticas descriptivas se usan en todos lados: notas escolares, analítica deportiva, investigación médica y KPIs empresariales. Esta calculadora toma cualquier lista de números y devuelve al instante todas las estadísticas clave: tendencia central, dispersión, cuartiles y más. Sin fórmulas que memorizar, sin hojas de cálculo.
Cómo usar la calculadora de estadísticas
- Ingresa tus números separados por comas (ej: 2, 4, 6, 8, 10).
- Haz clic en Calcular para ejecutar el análisis.
- Revisa todas las estadísticas en el panel de resultados: media, mediana, moda, rango, varianza, desviación estándar, Q1, Q3 e IQR.
- Usa las estadísticas individuales en tu informe, tarea o análisis de datos.
Fórmulas utilizadas
Media (μ): Σx / n
Mediana: valor central al ordenar (o promedio de los dos centrales)
Moda: valor más frecuente
Rango: máx − mín
Varianza: Σ(x − μ)² / n
Desv. estándar: √Varianza
Q1, Q3: percentiles 25 y 75
IQR: Q3 − Q1La desviación estándar poblacional divide entre n; la muestral divide entre (n − 1). Usa la poblacional cuando tienes todo el grupo; usa la muestral cuando trabajas con un subconjunto.
Ejemplos resueltos
Ejemplo 1: Conjunto {2, 4, 4, 4, 5, 5, 7, 9}
Media = (2+4+4+4+5+5+7+9) / 8 = 5,00. Mediana = promedio del 4.° y 5.° valor = (4+5)/2 = 4,50. Moda = 4 (aparece 3 veces). Rango = 9 − 2 = 7. Desv. estándar poblacional ≈ 2,00.
Ejemplo 2: Notas de examen {70, 80, 90, 100}
Media = (70+80+90+100) / 4 = 85,00. Mediana = (80+90)/2 = 85,00. Moda = ninguna (todos los valores aparecen una vez). Rango = 100 − 70 = 30. Desv. estándar = 11,18.
Ejemplo 3: Conjunto simétrico {1, 2, 3, 4, 5}
Media = 3,00. Mediana = 3,00. Moda = ninguna. Rango = 4. Cuando un conjunto es perfectamente simétrico, la media y la mediana son iguales — útil para detectar sesgo en datos reales.