How do you calculate the standard deviation?
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Lucas Turner
Works at the International Development Association, Lives in Washington, D.C., USA.
As a subject matter expert in statistics, I can guide you through the process of calculating the standard deviation, which is a measure of the amount of variation or dispersion of a set of values.
Here's how you calculate the standard deviation for a population:
1. Find the Mean: Calculate the mean (average) of the data set.
2. Subtract and Square: Subtract the mean from each data point and square the result (this gives you the squared differences).
3. Sum the Squared Differences: Add up all the squared differences.
4. Divide by N: Divide the sum of the squared differences by the number of data points (N) to get the variance.
5. Take the Square Root: Take the square root of the variance to get the standard deviation.
For a sample of a population, you would use a slightly different formula to estimate the population standard deviation:
1. Find the Mean: Calculate the mean of the sample data.
2. Subtract and Square: Subtract the mean from each sample data point and square the result.
3. Sum the Squared Differences: Add up all the squared differences.
4. Divide by N-1: Divide the sum of the squared differences by the number of data points minus one (N-1) to get the sample variance.
5. Take the Square Root: Take the square root of the sample variance to get the sample standard deviation.
Remember, when calculating for a sample, you use N-1 in the denominator, which is known as Bessel's correction. This adjusts for the fact that we are estimating the population standard deviation from a sample.
Now, let's translate that into Chinese:
Here's how you calculate the standard deviation for a population:
1. Find the Mean: Calculate the mean (average) of the data set.
2. Subtract and Square: Subtract the mean from each data point and square the result (this gives you the squared differences).
3. Sum the Squared Differences: Add up all the squared differences.
4. Divide by N: Divide the sum of the squared differences by the number of data points (N) to get the variance.
5. Take the Square Root: Take the square root of the variance to get the standard deviation.
For a sample of a population, you would use a slightly different formula to estimate the population standard deviation:
1. Find the Mean: Calculate the mean of the sample data.
2. Subtract and Square: Subtract the mean from each sample data point and square the result.
3. Sum the Squared Differences: Add up all the squared differences.
4. Divide by N-1: Divide the sum of the squared differences by the number of data points minus one (N-1) to get the sample variance.
5. Take the Square Root: Take the square root of the sample variance to get the sample standard deviation.
Remember, when calculating for a sample, you use N-1 in the denominator, which is known as Bessel's correction. This adjusts for the fact that we are estimating the population standard deviation from a sample.
Now, let's translate that into Chinese:
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Studied at the University of Amsterdam, Lives in Amsterdam, Netherlands.
To calculate the standard deviation of those numbers:Work out the Mean (the simple average of the numbers)Then for each number: subtract the Mean and square the result.Then work out the mean of those squared differences.Take the square root of that and we are done!
2023-04-12 08:05:21
Oliver Brown
QuesHub.com delivers expert answers and knowledge to you.
To calculate the standard deviation of those numbers:Work out the Mean (the simple average of the numbers)Then for each number: subtract the Mean and square the result.Then work out the mean of those squared differences.Take the square root of that and we are done!
