# What is the Difference Between Variance and Deviation?

The difference between variance and deviation is that the deviation (aka standard deviation) indicates how far individual points are from the average (mean). It’s expressed in squared units (e.g., metres, years). Whereas variance represents the average squared distance from the mean. It’s expressed in squared units (e.g., meters², years²).

## What is Variance?

Imagine a collection of leaves. Variance tells you how far each leaf is from the average leaf size. High variance means leaves vary greatly in size, while low variance indicates similar-sized leaves. In statistics, it’s the average of squared distances from the mean (average value). This table provides a comprehensive overview of variance, covering its definition, formula, properties, notation, interpretation, and calculation methods.

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## What is Deviation?

The standard deviation measures the spread of data from the mean, reflecting typical deviations. It returns to its original units, making it popular for variability assessment. Closed data to the mean yields a low deviation; spread data indicates a high variance. It’s affected by all values, making it independent of origin but not scale. It’s crucial in advanced statistical analyses. This table summarises the key aspects of standard deviation, including its definition, calculation formula, properties, interpretation, application, and an example scenario.

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## What is the Difference between Variance and Deviation

This table provides a concise overview of the differences between Variance and Standard Deviation, covering aspects such as definition, calculation formula, expression, mathematical notation, indicator of, measure of, nature of measure, calculation method, and application.

## Variance and Deviation Formulas

The average square distance between each data value and the mean value represents the data set’s variance, The distribution of data values around the mean is defined by the standard deviation. The population, as well as the sample variance formula, is given by:

Here,

• σ2 = Population variance
• N = Number of observations in population
• Xi = ith observation in the population
• μ = Population mean
• s2 = Sample variance
• n = Number of observations in the sample
• xi = ith observation in the sample
• σ = Population standard deviation
• s = Sample standard deviation

## Application of Variance and Deviation in Real Life

Variance and deviation, though similar, serve distinct purposes in real life.Below we have mentioned some real life applications of variance and standard deviation and explained them using examples:

• Variance: Imagine a bakery. Ovens might have slight temperature differences. Variance tells you how much bread baking times differ from the average. A high variance means some buns burn while others stay raw.
• Standard Deviation (deviation): It’s like a “spread meter.” In the bakery example, the standard deviation tells you how many buns fall within a specific time range around the average baking time. A low deviation indicates consistent baking, while a high one suggests uneven temperatures.

## FAQ’s

What is the difference between variance and deviance?

Variance measures dispersion around the mean in a dataset. Deviance assesses model fit in statistical analysis.

What is the difference between mean deviation and variation?

Mean deviation calculates the average absolute deviation from the mean. Variation indicates the overall spread or variability in data.

What is the difference between range variance and standard deviation?

The range shows the difference between max and min values. Variance computes average squared deviation. The standard deviation is its square root.

Is variance the deviation?

No, variance measures the average squared deviation from the mean. Deviation represents individual data point’s distance from the mean.

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