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. Related Statistics Calculator | Standard Deviation Calculator | Sample Size Calculator

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