Arithmetic mean a series of numbers is the quotient of dividing the sum of these numbers by the number of terms.
For row a1, a1. an arithmetic mean is calculated by the formula:
We find the arithmetic mean for the numbers 5.24, 6.97, 8.56, 7.32 and 6.23.
Range Numbers is the difference between the largest and smallest of these numbers.
The range of 5.24, 6.97, 8.56, 7.32, 6.23 is 8.56-5.24 =3.32
Fashion number series called the number that occurs in this series more often than others.
A series of numbers may have more than one mode, or may not have a mode at all.
The fashion of the series 32, 26, 18, 26, 15, 21, 26 is the number 26occurs 3 times.
Among the numbers 5.24, 6.97, 8.56, 7.32 and 6.23 there are no fashion.
Series 1, 1, 2, 2, 3 contains 2 modes: 1 and 2.
Median an ordered series of numbers with an odd number of members is called the number written in the middle, and the median of an ordered series of numbers with an even number of members is the arithmetic average of two numbers written in the middle.
The median of an arbitrary series of numbers is the median of the corresponding ordered series.
The median of series 4, 1, 2, 3, 3, 1 is 2.5.
Consider examples of finding the arithmetic mean of numbers, as well as the range, median and mode of the series.
How to find fashion in many numbers
In statistics fashion in a set of numbers called the number that is most often found in this set. There can be several modes: if two or more different numbers are found in the data set equally often, they are called accordingly bimodal or multimodal - in other words, all values occurring the maximum number of times form the modes of a given set. This article describes how to find the mode (s) of a set.
5.5 Fashion and median. Their calculation in discrete and interval variation series
Fashion and Med - a special kind of averages, which are used to study the structure of the variation series. They are sometimes called structural averages, in contrast to the previously considered power averages.
Fashion - this is the value of the sign (option), which is most often found in this population, i.e. has the highest frequency.
Fashion has great practical applications and in some cases only fashion can characterize social phenomena.
Median - This is a variant that is in the middle of an ordered variation series.
The median shows the quantitative limit of the value of the varying attribute, which reached half the units of the population. The use of the median along with the average or instead of it is advisable if there are open intervals in the variation series, since the calculation of the median does not require the conditional establishment of the boundaries of open intervals, and therefore the lack of information about them does not affect the accuracy of the calculation of the median.
The median is also used when the indicators that need to be used as weights are unknown. The median is used instead of the arithmetic mean for statistical methods of product quality control. The sum of the absolute deviations of the options from the median is less than from any other number.
Let us consider the calculation of the mode and median in a discrete variational series: