Note that in this particular data set, the addition of an outlier (a value well outside the expected range of values), the value 1,027,892, has no real effect on the data set. Since there are an even number of values, the median will be the average of the two middle numbers, in this case, 23 and 23, the mean of which is 23. If there were another value added to the data set:
Given the same data set as before, the median would be acquired in the following manner:Īfter listing the data in ascending order, and determining that there are an odd number of values, it is clear that 23 is the median given this case. 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. Related Statistics Calculator | Standard Deviation Calculator | Sample Size Calculator
0 kommentar(er)
