In the odd cases where there are only two data samples or there is an even number of samples where all the values are the same, the mean and median will be the same. While this can be confusing, simply remember that even though the median sometimes involves the computation of a mean, when this case arises, it will involve only the two middle values, while a mean involves all the values in the data sample. When the data sample contains an even number of values, the median is the mean of the two middle values. In the case where the total number of values in a data sample is odd, the median is simply the number in the middle of the list of all values. Conventionally, the values are listed in ascending order, but there is no real reason that listing the values in descending order would provide different results. Note that when calculating the median of a finite list of numbers, the order of the data samples is important.

Finding the median essentially involves finding the value in a data sample that has a physical location between the rest of the numbers. The statistical concept of the median is a value that divides a data sample, population, or probability distribution into two halves. In general, mean, median, mode and range should ideally all be computed and analyzed for a given sample or data set since they elucidate different aspects of the given data, and if considered alone, can lead to misrepresentations of the data, as will be demonstrated in the following sections. Proper understanding of given situations and contexts can often provide a person with the tools necessary to determine what statistically relevant method to use. Given the data set 10, 2, 38, 23, 38, 23, 21, applying the summation above yields: 10 + 2 + 38 + 23 + 38 + 23 + 21Īs previously mentioned, this is one of the simplest definitions of the mean, and some others include the weighted arithmetic mean (which only differs in that certain values in the data set contribute more value than others), and geometric mean. Similarly, or rather confusingly, the sample mean in statistics is often indicated with a capital X̄. In the specific case of the population mean, rather than using the variable x̄, the Greek symbol mu, or μ, is used.

The mean is often denoted as x̄, pronounced 'x bar,' and even in other uses when the variable is not x, the bar notation is a common indicator of some form of the mean. The equation for calculating the arithmetic mean is virtually identical to that for calculating the statistical concepts of population and sample mean, with slight variations in the variables used: In this form, the mean refers to an intermediate value between a discrete set of numbers, namely, the sum of all values in the data set, divided by the total number of values. In its simplest mathematical definition regarding data sets, the mean used is the arithmetic mean, also referred to as mathematical expectation, or average. Depending on the context, whether mathematical or statistical, what is meant by the 'mean' changes. The word mean, which is a homonym for multiple other words in the English language, is similarly ambiguous even in the area of mathematics.

Weisstein, Eric W., ' Triangle Median', MathWorld.Related Statistics Calculator | Standard Deviation Calculator | Sample Size Calculator.Constructing a median of a triangle with compass and straightedge animated demonstration.Medians of a triangle With interactive animation.Area of Median Triangle at cut-the-knot.Medians and Area Bisectors of a Triangle.↑ Leung, Kam-tim and Suen, Suk-nam 'Vectors, matrices and geometry', Hong Kong University Press, 1994, pp.↑ Benyi, Arpad, 'A Heron-type formula for the triangle', Mathematical Gazette 87, July 2003, 324–326.↑ Boskoff, Homentcovschi, and Suceava (2009), Mathematical Gazette, Note 93.15.↑ 5.0 5.1 Posamentier, Alfred S., and Salkind, Charles T., Challenging Problems in Geometry, Dover, 1996: pp.E., 'Halving a triangle,' Mathematical Gazette 56, May 1972, 105-108. There are four medians, and they are all concurrent at the centroid of the tetrahedron. A line segment joining a vertex of a tetrahedron with the centroid of the opposite face is called a median of the tetrahedron.

Let D be the midpoint of A B ¯ TetrahedronĪ tetrahedron is a three-dimensional object having four triangular faces. (Any other lines which divide the area of the triangle into two equal parts do not pass through the centroid.) The three medians divide the triangle into six smaller triangles of equal area.Ĭonsider a triangle ABC. Each median divides the area of the triangle in half hence the name, and hence a triangular object of uniform density would balance on any median.

Median geometry