As the term "median" refers the exact middle division of a set of values, this definition can also pertain to the geometrical shapes of triangles. Consider the two lines that meet at the corner or vertex of a triangle. Consequently, the exact middle point of the opposite side facing that vertex represents the median point of that side of the triangle.
In fact, three medians exist within a triangle as a result of possessing three corners, or vertices. Therefore, mathematicians have assigned the point of intersection of all these medians the name "centroid."
Another aspect of a mathematical median refers to the middle value within a number distribution. In considering a series of numbers, the determination of the median depends on whether the set of numerals is even or odd. In order to calculate the median, list the specified number set in numerical order—that is, least to greatest. If the number of terms is odd, the median is the exact middle value of the number set. On the other hand, if the number of terms is even, the average of two middle numbers will produce the median.
For instance, in a set of nine numbers such as (4, 4, 6, 9, 7, 7, 5, 8, 8), the median is the fifth number—in this case, 7.
However, in an even numbers set of even numbers, such as (3, 4, 4, 5, 6, 7, 7, 8, 8, 9) the median will be the average of two middle terms when arranging the set in numerical order. Find the median in this set of numerals by figuring the average of fifth and sixth number—that is, (6 + 7)—divided by 2, which comes to 6.5.
A descriptive statistic that represents mathematical data will possess a number of ideal properties. Statisticians agree that the numerical character designated as a median must be single valued and algebraically calculable, and the median product considers every observed value.
A median qualifies as a valid statistic by meeting some specific requirements. A median must be a single-value criterion, as the number of values above the median equal the number of values below the median. Calculate a median in an even set of data algebraically by finding the average of the two values that fall in the center of the numerically listed data in ascending order; find a median in a set of odd numerals graphically by merely determining the value that falls directly in the middle of the data set. Finally, consider all observed values in a specific data set when determining the median as a median value.
Median math is an algebraic concept, not to be confused with the task of determining the average of a set of data. Mathematicians prefer the practice of measuring central tendency, a more in-depth calculation and analysis of a numerical set. The median, along with the mean and the mode, is a detailed description of a numeric frequency.