Median is an important concept in mathematics and statistics, defined as the midpoint of a set of values. In a set of numbers, the median is the middle value that divides the data into two equal halves. It is a measure of central tendency, meaning the value that most accurately represents the entire data set. The median is typically used to measure the center of a data set that is not normally distributed.
In order to understand the median, it is important to first understand the concept of the “middle”. In a set of numbers, the middle value is the one that separates the higher half of the data from the lower half. For example, in a set of nine numbers, the middle value is the fifth number.
The median is calculated by first ordering the set of values from least to greatest. The median then is the middle value of the ordered set. If the set contains an even number of values, the median is calculated by taking the mean of the two middle values. The median is often used in place of the mean in cases where the data set is not normally distributed. This is because the median is not affected by outliers or extreme values, which can skew the mean and make it an inaccurate measure of central tendency.
In addition to its use in statistics, the median is also used in a variety of other disciplines, including economics, finance, and engineering. For example, in finance, the median is often used to measure the differences between two companies or stocks. In engineering, the median is used to measure the performance of a system over time.
The median is an important concept for anyone studying statistics or mathematics. It provides a measure of central tendency that is not affected by outliers or extreme values, making it an effective tool for analyzing data sets that are not normally distributed.
References
Ben-Zvi, D., & Garfield, J. (2003). The meaning and use of the median. The American Statistician, 57(1), 1–6. https://doi.org/10.1198/0003130031745
Hazewinkel, M. (2001). Median. In Encyclopedia of Mathematics. Springer, Berlin, Heidelberg. https://www.encyclopediaofmath.org/index.php/Median
Hines, T. (2008). Median. In Stat Trek. http://stattrek.com/statistics/dictionary.aspx?definition=median