Question
Download Solution PDFIf a constant is added to each observation of a data set, then which of the following measures of dispersion will change?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF- When a constant is added to each observation of a data set, the Coefficient of Variation (CV) will change.
- The Coefficient of Variation measures relative variability and is calculated as the ratio of the standard deviation to the mean, expressed as a percentage. Adding a constant to each observation will affect both the mean and the standard deviation. As a result, the ratio of the standard deviation to the norm, which is the Coefficient of Variation, will also change.
- The Coefficient of Variation is commonly used to compare the relative variability between different data sets or variables. When a constant is added to each observation, the relative variability, as measured by the Coefficient of Variation, will be altered. Therefore, the Coefficient of Variation will change when a constant is added to each observation in a data set.
Additional Information
- To calculate the Coefficient of Variation, divide the standard deviation by the mean and then multiply the result by 100 to express it as a percentage. The CV provides a relative measure of variability, allowing for comparison of the dispersion of different datasets or variables, regardless of their scales or units of measurement.
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CV = (Standard Deviation / Mean) * 100; Standard Deviation is the measure of dispersion that quantifies the average amount by which each data point varies from the mean. Mean is the average value of the data set. It is important to ensure that the mean and standard deviation are calculated based on the same set of data or population.
Last updated on Jul 17, 2025
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