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Calculez la variance et les mesures statistiques associées. Indispensable pour comprendre la dispersion et la variabilité des données en statistiques.
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Calculateur de Variance
Calculez la variance et les mesures statistiques associées. Indispensable pour comprendre la dispersion et la variabilité des données en statistiques.
Entrées
Entrez les valeurs requises pour le calcul
Résultats
Voir les résultats du calcul
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Qu'est-ce que Variance?
Variance mesure how far each nombre dans a set est de the mean. It est the square de standard deviation et représente the dispersion de données points around the mean. Variance est used dans risk assessment, portfolio theory, quality control, et statistical analysis. Sample variance (using n-1) provides un unbiased estimate quand working avec a sample de a larger population.
Comment utiliser
Enter your dataset values separated par commas, spaces, ou new lines. Select whether your données est une sample ou population. The calculateur displays variance, standard deviation, sum de squares, degrees de freedom, et provides interpretation de the variance level (low, moderate, high, ou very high).
Questions fréquentes
What is variance?
Variance is a statistical measurement that describes the spread of data points in a data set. It calculates how far each number in the set is from the mean (average). A higher variance indicates that the data points are more spread out from the mean, while a lower variance indicates they are closer to the mean.
What is the difference between Population and Sample variance?
Population variance calculates the variance for an entire dataset (every member of a specific group). Sample variance estimates the variance based on a subset of the population. The main mathematical difference is the denominator: Population variance divides by $N$ (total count), whereas Sample variance divides by $n-1$ (Bessel's correction) to provide a more accurate estimate of the population variance.
How do I format my data input?
You can enter numbers separated by commas, spaces, or new lines. For example, you can enter '10, 20, 30' or '10 20 30' or list them vertically. Ensure that you do not mix text characters with your numbers.
What is the formula used for this calculation?
For Population Variance ($\sigma^2$), the formula is $\frac{\sum(x_i - \mu)^2}{N}$. For Sample Variance ($s^2$), the formula is $\frac{\sum(x_i - \bar{x})^2}{n-1}$, where $x_i$ represents each value, $\mu$ and $\bar{x}$ are the mean, and $N$ and $n$ are the number of data points.
Why does the result show 'NaN' or 'Error'?
This usually happens if the input field is empty, contains non-numeric characters (like letters or symbols), or if you are trying to calculate Sample variance with only one data point (as division by zero is undefined).
Can I calculate variance for grouped data?
This calculator is designed for raw data lists (ungrouped data). To calculate variance for grouped data, you would need to calculate the weighted mean first, then apply the specific grouped variance formula, which is not supported by this standard input format.
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