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# What are some real-world examples of direct variations?

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Direct variation exists when a worker is paid based on the number of hours worked. Another example of a direct variation is a taxi fare that varies according to the distance traveled. Direct variation occurs with two variables when the ratio of their values always remains the same. For example, if the value of A is always twice as much as B, they vary directly.

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Credit: Sebastiaan Ter Berg CC-BY-SA 2.0

Direct variation can be expressed as an equation, an algebraic expression or a geometric expression. To illustrate the concept of direct variation as an equation, take the equation y/x = 6. Y varies directly with X, with 6 being the constant in the equation. From the equation, it can be determined that Y is always six times greater than X. The equation y = kx is an example of an algebraic equation that illustrates direct variation. Both Y and X are always multiplied by the same amount. This equation is a linear equation. In addition to direct variations, other relationships between numbers and variables that remain constant exist in the mathematical world. Variables A and B are said to be inversely related to each other when A varies as the reciprocal of B. Variables can also be jointly related.

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## Related Questions

• A:

The coefficient of variation is used in statistics to measure distribution. It can be found from the ratio of the standard deviation over the mean of a set of numbers to calculate both probability and frequency. When it is used in finance, the mean is considered the expected return.

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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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Coefficient of variation is defined as the ratio of standard deviation to the arithmetic mean. Coefficient of variation gives a sense of "relative variability," as reported by the GraphPad Statistical software website. It can be expressed either as a fraction or a percent.