Average

Average

Video: Math Help : How to Calculate an Average

Different concepts of average are used in different contexts. Often "average" refers to the arithmetic mean, the sum of the numbers divided by how many numbers are being averaged. In statistics, mean, median, and mode are all known as measures of central tendency, and in colloquial usage sometimes any of these might be called an average value.

Arithmetic mean

Video: What is the Arithmetic Mean?

If n numbers are given, each number denoted by a_i (where i = 1,2, …, n), the arithmetic mean is the sum of the as divided by n or

$${\displaystyle AM={\frac {1}{n}}\sum _{i=1}^{n}a_{i}={\frac {1}{n}}\left(a_{1}+a_{2}+\cdots +a_{n}\right)}

The arithmetic mean, often simply called the mean, of two numbers, such as 2 and 8, is obtained by finding a value A such that 2 + 8 = A + A. One may find that A = (2 + 8)/2 = 5. Switching the order of 2 and 8 to read 8 and 2 does not change the resulting value obtained for A. The mean 5 is not less than the minimum 2 nor greater than the maximum 8. If we increase the number of terms in the list to 2, 8, and 11, the arithmetic mean is found by solving for the value of A in the equation 2 + 8 + 11 = A + A + A. One finds that A = (2 + 8 + 11)/3 = 7.

Mode

 

Comparison of arithmetic mean, median and modeof two log-normal distributions with different skewness

Video: The Mean, Median and Mode Toads

For example, the mode of the list (1, 2, 2, 3, 3, 3, 4) is 3. It may happen that there are two or more numbers which occur equally often and more often than any other number. In this case there is no agreed definition of mode. Some authors say they are all modes and some say there is no mode.

Median

Video: Statistics - Find the median

Thus to find the median, order the list according .....

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