Stats Ch 2.4 Measures of Variation

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What is a measure of variability?

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A measure of variability quantifies the extent to which data points in a dataset differ from each other. Common measures include range, variance, and standard deviation.

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What is standard deviation?

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Standard deviation is a statistic that measures the dispersion of a dataset relative to its mean. A low standard deviation indicates that data points tend to be close to the mean, while a high standard deviation indicates a wider spread.

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What percentage of data falls within one standard deviation of the mean in a normal distribution?

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Approximately 68% of the data falls within one standard deviation of the mean in a normal distribution.

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What percentage of data falls within two standard deviations of the mean in a normal distribution?

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Approximately 95% of the data falls within two standard deviations of the mean in a normal distribution.

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What is a normal distribution?

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A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

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What does it mean if a distribution is skewed left?

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A left-skewed distribution has a longer tail on the left side, indicating that there are a larger number of lower values compared to higher values.

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What is the formula for calculating the mean?

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The mean is calculated by summing all the values in a dataset and dividing by the number of values.

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How do you find the height of an unknown student if the mean is known?

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To find the height of the unknown student, multiply the mean height by the total number of students, subtract the sum of the known heights, and solve for the unknown height.

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What is variance?

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Variance is a measure of how far a set of numbers are spread out from their average value. It is the average of the squared differences from the mean.

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What is the range of a dataset?

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The range is the difference between the highest and lowest values in a dataset.