Average
The word “average” is used in everyday life to describe where the middle number of a data set is. It’s the typical number you would expect to find in a series of numbers. In statistics, the average is called the “arithmetic mean,” usually just shortened to the mean. Both the average and the mean use the same formula:
avg = total sum of all the numbers / number of items in the set.
Example
You earned $129, $139, $155 and $176 over the last 4 weeks. What is your average pay?
- Add up all of the numbers in the set. $129 + $139 + $155 + $176 = $599.
- Divide Step 1 by the total number of items in the set. There are 4 items in the set, so $599 / 4 = $149.75.
In probability and statistics, you’ll see the following formula used:
Airthmatic , geomatric and harmonic means
Airthmatic mean
The arithmetic mean is the simplest and most widely used measure of a mean, or average. It simply involves taking the sum of a group of numbers, then dividing that sum by the count of the numbers used in the series.
For example take 34, 44, 56 and 78. The sum is 212. The arithmetic mean is 212 divided by four, or 53.
The arithmetic mean maintains its place in finance, as well. For example, mean earnings estimates typically are an arithmetic mean. Say you want to know the average earnings expectation of the 16 analysts covering a particular stock. Simply add up all the estimates and divide by 16 to get the arithmetic mean.
The same is true if you want to calculate a stock’s average closing price during a particular month. Say there are 23 trading days in the month. Simply take all the prices, add them, up and divide by 23 to get the arithmetic mean.
The arithmetic mean is simple, and most people with even a little bit of finance and math skill can calculate it. It’s also a useful measure of central tendency, as it tends to provide useful results, even with large groupings of numbers.
Geomatric mean
The Geometric mean is defined as the nth square root of the product of n distinct data values. That is, consider, n data values as x1, x2, …, xn the geometric mean is given by,
Moreover, geometric mean is considered as a special type of average. Also, the value of geometric is less than the arithmetic mean and is considered as one of the measures of central tendency.
Also, if the n data values has repeated values x1, x2,…, xm with frequencies f1,f2,…,fm, then the geometric mean is given by,
The other formula to calculate the geometric mean is,
Harmonic mean
The harmonic mean is a very specific type of average. It’s generally used when dealing with averages of units, like speed or other rates and ratios.
formula is:
