Standard Deviation Practice

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What is standard deviation?

Back

A measure of the amount of variation or dispersion in a set of values.

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How is standard deviation calculated?

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1. Find the mean of the data set. 2. Subtract the mean from each data point and square the result. 3. Find the average of these squared differences. 4. Take the square root of that average.

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What does a low standard deviation indicate?

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The data points tend to be close to the mean, indicating low variability.

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What does a high standard deviation indicate?

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The data points are spread out over a wider range of values, indicating high variability.

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What is the formula for standard deviation (population)?

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σ = √(Σ(xi - μ)² / N) where μ is the mean, N is the number of data points.

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What is the formula for standard deviation (sample)?

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s = √(Σ(xi - x̄)² / (n - 1)) where x̄ is the sample mean and n is the sample size.

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What is the relationship between variance and standard deviation?

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Standard deviation is the square root of variance.

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How does standard deviation relate to the normal distribution?

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In a normal distribution, about 68% of data falls within one standard deviation of the mean.

Tags

CCSS.HSS.ID.A.4

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What is the effect of outliers on standard deviation?

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Outliers can significantly increase the standard deviation, indicating greater variability.

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How can standard deviation be used in real-life applications?

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It can be used in finance to assess risk, in education to evaluate test scores, and in quality control to monitor processes.