Math What is the average

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Finding the average Finding the average or the mean is a very straightforward concept. If you have a set of numbers, the average is found by adding all numbers in the set and dividing their sum by the total number of numbers added in the set.

We can generalize the concept of average with the formula below: Let x 1 ,x 2 ,x 3 , When the numbers in the set are all the same, the average is just the number itself. Whole numbers Average word problems.

Recent Articles. Like the median and the mode , the average is a measure of central tendency, meaning it reflects a typical value in a given set. Averages are used quite regularly to determine final grades over a term or semester. Averages are also used as measures of performance. For example, batting averages express how frequently a baseball player hits when they are up to bat. Gas mileage expresses how far a vehicle will typically travel on a gallon of fuel.

In its most colloquial sense, average refers to whatever is considered common or typical. A mathematical average is calculated by taking the sum of a group of values and dividing it by the number of values in the group. It is also known as an arithmetic mean.

Other means, such as geometric and harmonic means, are calculated using the product and reciprocals of the values rather than the sum. With a small set of values, calculating the average takes only a few simple steps.

For example, let us imagine we want to find the average age among a group of five people. Their respective ages are 12, 22, 24, 27, and First, we add up these values to find their sum:. Then we take this sum and divide it by the number of values 5 :. The result, 24, is the average age of the five individuals. The average, or mean, is not the only measure of central tendency, though it is one of the most common. The other common measures are the median and the mode. The median is the middle value in a given set, or the value that separates the higher half from the lower half.

In the example above, the median age among the five individuals is 24, the value that falls between the higher half 27, 35 and the lower half 12, In the case of this data set, the median and the mean are the same, but that is not always the case.

For example, if the youngest individual in the group were 7 instead of the 12, the average age would be However, the median would still be For statisticians, the median can be a very useful measure, especially when a data set contains outliers, or values that greatly differ from the other values in the set.

In the example above, all of the individuals are within 25 years of each other. But what if that were not the case? What if the oldest person were 85 instead of 35? That outlier would bring the average age up to 34, a value greater than 80 percent of the values in the set.

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