# Calculating variance from range

• Dawei
In summary, the conversation discusses the possibility of calculating the variance with limited information, specifically the average concentration and range of 5 sample data points. While it is not possible to calculate the variance without the standard deviation, it may be possible to estimate it if the shape of the distribution is known. One method suggested is to take the sum of the squares of the differences between the individual points and the average, and then divide by 4 to obtain an unbiased estimate for the variance.
Dawei
Hello,

I have taken 5 samples and found that my average concentration is 5 mg, with a range of .003 mg in either direction. I would like to calculate the variance with only this information.

Is this possible? I am used to calculating the variance from the standard deviation, but I don't have this available.

No, it's not possible. But if you know about the shape of the distribution you may be able to estimate the variance.

You can use the 5 sample data points to estimate the variance. Take the sum of the squares of the differences between the individual points and the average. Then divide by 4 (n-1 in general). This is an unbiased estimate for the variance.

## What is variance and how is it calculated?

Variance is a measure of how spread out a set of data is. It is calculated by taking the sum of the squared differences between each data point and the mean, and then dividing by the number of data points.

## How is variance different from range?

Range is a measure of the difference between the highest and lowest values in a set of data, while variance takes into account all the values in the data set to determine the spread. Range is a simple measure of spread, while variance is a more comprehensive measure that considers each data point.

## Can variance be negative?

No, variance cannot be negative. Since it is calculated by squaring the differences between data points and the mean, all values are positive. A negative result would indicate an error in calculation.

## Why is variance important in statistics?

Variance is important in statistics because it allows us to quantify the spread or variability of a dataset. It helps us understand how much the data points deviate from the mean, and can provide insights into the distribution and patterns within the data.

## How does sample size affect the calculation of variance?

Sample size can affect the calculation of variance. As the sample size increases, the variance will tend to decrease, since there are more data points to consider. A larger sample size can provide a more accurate representation of the population and reduce the impact of outliers on the variance calculation.

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