Mean deviation, also known as average deviation, is a statistical measure that quantifies the dispersion or variability of a set of data points. It measures how spread out the values are from the mean or average of the data set. Mean deviation is calculated by finding the average of the absolute differences between each data point and the mean.
The concept of mean deviation was introduced by the Italian mathematician and astronomer Giovanni Cassini in the 17th century. However, it was later refined and popularized by the French mathematician Adrien-Marie Legendre in the 18th century.
Mean deviation is typically introduced in middle or high school mathematics courses. It requires a basic understanding of arithmetic operations, such as addition, subtraction, and division. Additionally, knowledge of calculating the mean or average of a set of numbers is necessary.
There are two types of mean deviation: population mean deviation and sample mean deviation. Population mean deviation is used when the entire population is known, while sample mean deviation is used when only a subset or sample of the population is available.
To calculate mean deviation, follow these steps:
The formula for mean deviation is as follows:
Where:
To apply the mean deviation formula, substitute the values of the data points and the mean into the formula. Then, calculate the absolute differences and find their mean.
The symbol or abbreviation commonly used for mean deviation is "MD".
There are several methods to calculate mean deviation, including the direct method, the shortcut method, and the step deviation method. These methods provide alternative approaches to simplify the calculation process.
Q: What is the mean deviation? Mean deviation is a statistical measure that quantifies the dispersion or variability of a set of data points.
Q: How is mean deviation calculated? Mean deviation is calculated by finding the average of the absolute differences between each data point and the mean.
Q: What is the difference between population mean deviation and sample mean deviation? Population mean deviation is used when the entire population is known, while sample mean deviation is used when only a subset or sample of the population is available.
Q: Is mean deviation affected by outliers? Yes, mean deviation is affected by outliers or extreme values in the data set.