What is the difference between population and sample standard deviation?

Population standard deviation measures the spread of an entire population, using all data points. Sample standard deviation estimates the spread of a population based on a sample, using n-1 in the denominator to correct bias. Use population when you have all data, sample when you have a subset.

How do I use the standard deviation calculator?

Enter your data values separated by commas or spaces. The calculator will compute both population and sample standard deviation, along with variance. Ensure you enter numeric values only and separate them correctly.

What does variance mean in statistics?

Variance is the average of the squared differences from the mean. It measures how far each number in the set is from the mean. Standard deviation is the square root of variance, providing a measure of spread in the same units as the data.

Matematicas

Instantáneo, privado y gratis

Calculadora de Desviacion Estandar.

Calcula la desviacion estandar poblacional y muestral con varianza

Cálculo en el dispositivoSin registro

Introduce tus valores

Los resultados se actualizan al escribir.

02 / RESPUESTA

Ingresa Numeros(Ingresa numeros separados por comas, espacios o lineas nuevas)

Poblacion (σ)

Desviacion Estandar Poblacional (σ): Usa cuando tienes datos de toda la poblacion. Divide por N.

Muestra (s)

Desviacion Estandar Muestral (s): Usa cuando tienes una muestra de una poblacion mayor. Divide por N-1 (correccion de Bessel).

Muestra Resultados

Media (μ)18.0000

Varianza (s²)27.4286

Desviacion Estandar (s)5.2372

Resultados

Cantidad (n)8

Suma (Σx)144.00

Median18.5000

Mode23

Rango13.00

Minimo / Maximo10 / 23

Datos Ordenados

10, 12, 16, 16, 21, 23, 23, 23

Entendiendo la Desviacion Estandar

Interpretacion: Una desviacion estandar baja significa que los datos estan cerca de la media. Una alta significa que los datos estan dispersos en un rango mas amplio.

Poblacion vs. Muestra: Desviacion Estandar Poblacional (σ): Usa cuando tienes datos de toda la poblacion. Divide por N. Desviacion Estandar Muestral (s): Usa cuando tienes una muestra de una poblacion mayor. Divide por N-1 (correccion de Bessel).

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Cite this calculator

Canonical URL: https://mathify.one/es/math/standard-deviation

Cite as: Mathify. (n.d.). Calculadora de Desviacion Estandar. https://mathify.one/es/math/standard-deviation

Use Cases

Analyze test scores

Teachers and students can use the calculator to understand the spread of exam results, identifying how consistent performance is across a class.

Example: Enter scores like 85, 90, 78, 92, 88 to see the standard deviation.

Quality control in manufacturing

Engineers can measure variability in product dimensions or weights to ensure consistency and meet quality standards.

Example: Input measurements like 10.2, 10.5, 10.1, 10.3 to check process variability.

Frequently Asked Questions

What is the difference between population and sample standard deviation?: Population standard deviation measures the spread of an entire population, using all data points. Sample standard deviation estimates the spread of a population based on a sample, using n-1 in the denominator to correct bias. Use population when you have all data, sample when you have a subset.
How do I use the standard deviation calculator?: Enter your data values separated by commas or spaces. The calculator will compute both population and sample standard deviation, along with variance. Ensure you enter numeric values only and separate them correctly.
What does variance mean in statistics?: Variance is the average of the squared differences from the mean. It measures how far each number in the set is from the mean. Standard deviation is the square root of variance, providing a measure of spread in the same units as the data.

Tips & Common Mistakes

Tips

Ensure your data is numeric and separated by commas or spaces for accurate calculation.
Use population standard deviation when your data represents the entire group; use sample for a subset.
Check for outliers before interpreting standard deviation, as extreme values can inflate the result.
Remember that standard deviation is always non-negative; a value of 0 means all data points are identical.

Common Mistakes to Avoid

Confusing population and sample standard deviation, leading to incorrect conclusions.
Entering non-numeric characters or mixing delimiters, causing errors in calculation.
Using standard deviation to compare datasets with different units or scales without proper normalization.

Last updated: August 13, 2026