What Does Average Mean?
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We can define average as the fraction of the summation of whole data to the number of units. In other words, the average is the midpoint or central point of any data. Another meaning of average can be “the mean value that is equivalent to the ratio between the total numbers of a specific set and the total numbers in the given set”. In mathematics or statistics, if you want to find the average of any data you have to find the sum of all the values and then divide the summed up value by the total number of values in the given data.
Throughout the years and after plenty of research and study, mathematicians were able to deduce three convenient ways of calculating the average of a set of data. The first one is called the mean, which is sometimes used instead of the term “average”, second is the median, and third is the mode of the data. The majority of the mathematical applications use the term average which automatically means to calculate the mean. Considered as one of the basic concepts of mathematics, the average can be obtained using basic mathematical operations of addition and division.
What is The Symbol for Average?
The average symbol in math is commonly a Greek Letter “μ” (mu). Since the average and mean are similar terms, you will also see the average symbol written as x¯ (x bar). In statistics, μ is generally used to calculate the population meanwhile x¯ is used for the sample mean.
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Average Symbol 2023
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All Symbols that can be used for average:
μ μx x̅ x-bar mu Σ ω φ μ ∀ ∃
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Types Of Average
The term “average” can be divided into 2 categories, and each of them has different formulas. However, the average symbol remains the same for every type.
1. Mathematical average
It is the most common type of average which is subdivided into many different types, which are:
A. Arithmetic Mean
It is the most widely used measure to calculate average. To calculate the arithmetic mean, you need to take the sum of values and divide it by the total number of values in the group. However, in finance, this type isn’t the perfect measure to calculate the average as it can highly skew the mean value. And if you’re wondering what is the symbol for mean, then the average symbol for this type is also the same. i.e the Greek letter μ for the population mean and x – (x bar) for the sample mean. Apart from the above Greek symbol for average, there is a mathematical symbol called “ Sigma notation” which is a Greek capital letter sigma: Σ.
B. Geometrical Mean
The geometric mean is a way to discover the central tendency of a set of numbers by finding the nth root of the product of n numbers. It is far more distinct than the arithmetic mean, in which we add the observations and then divide the sum by the number of observations. However, the geometric mean allows us to find the product of all the observations and then calculate the nth root of the product, given that n is the number of observations.
C. Harmonic Mean
The other name for numerical average is the harmonic mean. You can find out the harmonic mean by dividing the total number of values by the reciprocal of every number in the set. In other words, harmonis mean is the reciprocal of the average of the reciprocals of the values. It is often used to calculate average rates or where there is a need to give weightage to smaller items.
2. Positional Average
If an average is calculated through the observation from a series from which a single figure is selected representing the series as a whole, such as the case of positional average. For this reason, median and mode are considered as positional averages.
The middle number of the sorted list is called the median. To calculate the median of a sequence of numbers, you first need to sort the figures in the order of lowest to highest or highest to lowest.
Apart from mean and median as a popular measure for central tendency, mode is one of them too. The value appearing frequently in a data set is considered as the mode. There can be no mode, one mode or multiple modes in the given data set. It is a handy way to measure the central tendency for observing categorical data.
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Calculation of average is useful in daily life as it summarizes a large number of data in a single value. It also gives a general idea of how other figures in a data set are performing as a whole. Depending on the data provided, one can use any of the three types of averages. Along with that, the average symbol for most of the types is also the same i.e “x-bar”.