Q:

How do you calculate standard deviation?

A:

Quick Answer

To calculate the standard deviation, take the square root of the variance. Find the variance by calculating the average of the squared differences from the average of the set.

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Full Answer

  1. Find the average value of the data set

    To find the average value, add up all the data points in the set, and then divide by the number of data points. For example, in a data set of 4, 6, 7, 1 and 12, add up all five data points to find the sum of 30, then divide by 5 to find the average value of 6.

  2. Calculate the squared differences

    To calculate the squared differences, subtract each number in the data set from the average value, and square it. In the example data set from Step 1, the first squared difference is (6-4)^2=4. The second squared difference is (6-6)^2=0. Find a squared difference for each data point in the data set.

  3. Find the variance

    Find the variance by calculating the average of all the squared differences you found in Step 2. To do this, add up all the squared differences, and then divide the sum by the number of values in the set. In the example, the squared differences are 4, 0, 1, 25 and 36. The average of the squared differences is the sum of the values (66) divided by the number of data points (5). Therefore, 13.2 is the variance.

  4. Take the square root of the variance

    Find the standard deviation by taking the square root of the variance. In the example, 13.2 is the variance, so the standard deviation is the square root of 13.2, which is 3.6.

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Related Questions

  • Q:

    Why do we use standard deviation?

    A:

    Standard deviation is a measure of the variation or diversity of scores in a set of data. It is used to determine how much data varies from the average of a population. The larger the deviation, the more spread out the data set. Standard deviation is represented by the Greek letter sigma.

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  • Q:

    How do you find the standard deviation?

    A:

    To calculate standard deviation, calculate the mean of the sample numbers by adding them up and dividing by the number of terms. Subtract the mean from each number and square the result. Add up these numbers and divide by the number of terms for the variance. The square root of this is the standard deviation.

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  • Q:

    What is the geometric standard of deviation?

    A:

    Geometric standard deviation is the degree of variance of a particular group of numbers from the geometric mean as opposed to the binomial mean. It is appropriately used for numbers that form a geometric distribution rather than a binomial one.

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  • Q:

    What is the importance of standard deviation?

    A:

    Standard deviation is a measure of variation in data. It allows comparison between two or more sets of data to determine if their averages are truly different. For example, if the average salaries in two companies are $90,000 and $70,000 with a standard deviation of $20,000, the difference in average salaries between the two companies is not statistically significant.

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