# Central Tendency Statistics The most typical measures of central tendency tend to be the arithmetic mean, the mode and the median. A central tendency can be determined for either a finite pair of values or for a theoretical distribution, including the normal distribution.

Solutions to variational problems

A number of measures of central tendency could be characterized as fixing a variational problem, in the sense of the calculus of variations, namely reducing variation from the center. That is, given a measure of statistical dispersion, one requests for a measure of central tendency which minimizes variation: such that variation through the center is minimal between all choices of center.

## Central Tendency and Dispersion

Central tendency and dispersion means idea that there is a single number that best summarizes the entire pair of measurements, a number that is in some manner central to the set.

The mode. The mode is the measurement which has the greatest frequency, the one you found the most of. Although it is not used much, it is helpful when differences are rare or once the differences are non numerical. The prototypical instance of something is generally the mode.

The mode for our example is 3.2. It is the grade with the many people (3).

The median. The median is the number where half your measurements are greater than that number and half are lower than that number. The median is in fact a better measure of centrality than the mean if your data are skewed, which means lopsided.

The mean. The mean is only the average. It is the amount of all your measurements, separated by the number of measurements. This is the most employed measure of central tendency, due to its mathematical qualities.

## Central Tendency and Variability

Central tendency is actually a statistical measure which identifies an individual score as representative of a whole distribution of scores. The purpose of central tendency is to locate the single score that is most representative or most typical of the whole distribution.

Unfortunately, there is no single, standard process for figuring out central tendency. The issue is that there is no single measure that will always create a central, representative value in every situation. You can find three main measures of central tendency: the arithmetical mean, the mode and the median.

Variability gives a quantitative measure of the degree to which scores within a distribution are spread out. The higher the difference among scores, the greater spread out the distribution is. The more tightly the scores team together, the less variability there is within the distribution. Variability is the essence of statistics. The most often used techniques of measurement of this variance are: deviation, range and variance, standard deviation and interquartile range.

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