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What is a median in math

What is a median in math

What is a median in math

A median is the point where an equal number of items can be arranged in a horizontal line. Median is a type of value that is put in order according to size and shape so that half of the items in the set fall above it, and half fall below it.Students often find that it is easy to confuse the mean, median, and mode. While all are measures of central tendency, there are important differences in what each one means and how they are calculated. Explore some useful tips to help you distinguish between the mean, median, and mode and learn how to calculate each measure correctlyHow do you determine whether to use the mean, median, or mode? Each measure of central tendency has its own strengths and weaknesses, so the one you choose to use may depend largely on the unique situation and how you are trying to express your data

MEAN

The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers. The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order from smallest to largest, so you may have to rewrite your list before you can find the median. The "mode" is the value that occurs most often. If no number in the list is repeated, then there is no mode for the list. (In the above, I've used the term "average" rather casually. The technical definition of what we commonly refer to as the "average" is technically called "the arithmetic mean": adding up the values and then dividing by the number of values. Since you're probably more familiar with the concept of "average" than with "measure of central tendency", I used the more comfortable term.)

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic feature of the median in describing data compared to the mean (often simply described as the "average") is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of a "typical" value. Median income, for example, may be a better way to suggest what a "typical" income is, because income distribution can be very skewed. The median is of central importance in robust statistics, as it is the most resistant statistic, having a breakdown point of 50%: so long as no more than half the data are contaminated, the median is not an arbitrarily large or small result. For practical purposes, different measures of location and dispersion are often compared on the basis of how well the corresponding population values can be estimated from a sample of data. The median, estimated using the sample median, has good properties in this regard. While it is not usually optimal if a given population distribution is assumed, its properties are always reasonably good. For example, a comparison of the efficiency of candidate estimators shows that the sample mean is more statistically efficient when — and only when — data is uncontaminated by data from heavy-tailed distributions or from mixtures of distributions. (Source: en.wikipedia.org)

MEDIAN

The median is 2 in this case, (as is the mode), and it might be seen as a better indication of the center than the arithmetic mean of 4, which is larger than all-but-one of the values. However, the widely cited empirical relationship that the mean is shifted "further into the tail" of a distribution than the median is not generally true. At most, one can say that the two statistics cannot be "too far" apart; see § Inequality relating means and medians below. For practical purposes, different measures of location and dispersion are often compared on the basis of how well the corresponding population values can be estimated from a sample of data. The median, estimated using the sample median, has good properties in this regard. While it is not usually optimal if a given population distribution is assumed, its properties are always reasonably good. For example, a comparison of the efficiency of candidate estimators shows that the sample mean is more statistically efficient when — and only when — data is uncontaminated by data from heavy-tailed distributions or from mixtures of distributions.

Finding the TI 83 mean or TI 83 median from a list of data can be accomplished in two ways: by entering a list of data, or by using the home screen to type the commands. Using the list feature is just as easy as entering the data onto the home screen, and it has the added advantage that you can use the data for other purposes after you have calculated your mean, mode and median (for example, you might want to create a TI 83 histogram).There are other types of means. A geometric mean is found by multiplying all values in a list and then taking the root of that product equal to the number of values (e.g., the square root if there are two numbers). The geometric mean is typically used in cases of exponential growth or decline (see exponential function). In statistics, the mean of a random variable is its expected value—i.e., the theoretical long-run arithmetic mean of the outcomes of repeated trials, such as a large number of tosses of a die. For data that is grouped together (e.g., where values are 1–5, 6–10,…), the methods used for calculating the mean, median, and mode are different from those used for ungrouped data (e.g., where values are 1, 2, 3,…). (Source: www.britannica.com)

 

 

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