In colloquial language, an average is a middle or typical number of a list of numbers.
Video: Math Help : How to Calculate an Average
Different concepts of average are used in different contexts. Often "average" refers to thearithmetic mean, the sum of the numbers divided by how many numbers are being averaged. In statistics, mean,median, andmodeare all known asmeasuresofcentral tendency, and in colloquial usage sometimes any of these might be called an average value.
Arithmetic mean
The most common type of average is the arithmetic mean.
Video: What is the Arithmetic Mean?
Ifnnumbers are given, each number denoted byai(wherei = 1,2, …, n), the arithmetic mean is thesumof theas divided bynor
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 thatA= (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 ofAin the equation 2 + 8 + 11 = A + A + A. One finds thatA= (2 + 8 + 11)/3 = 7.
The most frequently occurring number in a list is called the mode.
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
The median is the middle number of the group when they are ranked in order. (If there are an even number of numbers, the mean of the middle two is taken.)
Video: Statistics - Find the median
Thus to find the median, order the list according .....