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HomeHomework HelpstatisticsMeasures of Variation

Measures of Variation

Quantitative methods used to describe the spread or dispersion of data, including range, variance, and standard deviation, which help understand how values are distributed within a dataset

intermediate
2 hours
Statistics
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Overview

Measures of variation are essential tools in statistics that help us understand the spread of data. They include range, variance, standard deviation, and interquartile range, each providing unique insights into how data points differ from one another. Understanding these measures allows us to make i...

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Key Terms

Range
The difference between the highest and lowest values in a data set.

Example: In the data set {3, 7, 5}, the range is 7 - 3 = 4.

Variance
A measure of how much the values in a data set differ from the mean.

Example: If the mean is 5 and the values are {3, 5, 7}, the variance is 2.

Standard Deviation
The square root of the variance, indicating how much the values deviate from the mean.

Example: A standard deviation of 2 means most values are within 2 units of the mean.

Interquartile Range (IQR)
The difference between the first quartile (Q1) and the third quartile (Q3) in a data set.

Example: For the data set {1, 3, 5, 7, 9}, Q1 is 3 and Q3 is 7, so IQR = 7 - 3 = 4.

Outlier
A data point that is significantly different from other observations.

Example: In the set {1, 2, 2, 3, 100}, 100 is an outlier.

Mean
The average of a set of numbers, calculated by dividing the sum of the values by the count.

Example: The mean of {2, 4, 6} is (2+4+6)/3 = 4.

Related Topics

Descriptive Statistics
Descriptive statistics summarize and describe the features of a data set.
intermediate
Probability Distributions
Probability distributions describe how the values of a random variable are distributed.
advanced
Inferential Statistics
Inferential statistics use a random sample of data to make inferences about the population.
advanced

Key Concepts

RangeVarianceStandard DeviationInterquartile Range