Standard Deviation

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What is Standard Deviation?

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Standard Deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.

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How do you calculate the mean of a data set?

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To calculate the mean, sum all the values in the data set and then divide by the number of values.

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What is the formula for Standard Deviation?

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The formula for Standard Deviation (σ) is: σ = √(Σ(xi - μ)² / N), where μ is the mean, xi represents each value, and N is the number of values.

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What does a standard deviation of 0 indicate?

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A standard deviation of 0 indicates that all values in the data set are identical and there is no variation.

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What is the difference between population standard deviation and sample standard deviation?

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Population standard deviation is calculated using all members of a population, while sample standard deviation is calculated using a subset of the population.

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How does standard deviation relate to the normal distribution?

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In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

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What is variance?

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Variance is the square of the standard deviation and measures the spread of a set of numbers.

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How do you find the median of a data set?

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To find the median, arrange the data in ascending order and identify the middle value. If there is an even number of values, the median is the average of the two middle values.

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What is the relationship between mean, median, and mode in a normal distribution?

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In a normal distribution, the mean, median, and mode are all equal.

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What is an outlier?

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An outlier is a data point that differs significantly from other observations in the data set, which can affect the mean and standard deviation.