Question

What do you understand by mean in statistics?

Answer 1

Hint: Mean is the average or the most common value in a collection of data. We will try to understand the concept of mean and the different ways to calculate the same, that is arithmetic mean and geometric mean.

Complete step-by-step solution:
In mathematics, we know that mean is an essential concept that is part of statistics. It represents a numerical representation of the given data set. In simple terms we can say that it is the value that is the most common one present in the data set. We will also observe that the mean is not among the actual values present in the given data set. We can also notice that one of its important properties is that it minimises error in the prediction of any one value in the given data set. That is, it is the value that produces the lowest amount of error from all other values in the given data set.
We should remember that mean is also known as the average of a data set and it’s value can be found by adding all the values of the observations stated in the given data set and then dividing it by the number of observations in the set. We should also remember that there are different ways of measuring the mean or the central tendency of a given set of observations. We have to remember that the mean can be calculated for grouped as well as ungrouped data. If the data is grouped, we have to consider the frequency to find the mean. As mentioned, we know there are multiple ways to calculate the mean. Let us consider two of the most commonly used ones: arithmetic mean and geometric mean.
1) Arithmetic mean is the total of the sum of all values of the observations in a collection divided by the number of observations in the collection. We should remember that it can be calculated by using the following formula.
\[Arithmetic\,Mean=\dfrac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}....+{{x}_{n}}}{n}\]
Where x is the values of the observations in the data and n is the total number of observations of the data.
2) Geometric mean is an nth root of the product of all observations in a collection. We should remember the formula to calculate the geometric mean as:
\[Geometric\,Mean=\sqrt[n]{{{x}_{1}}\times {{x}_{2}}\times {{x}_{3}}....\times {{x}_{n}}}\]

Note: We should note the mean has some disadvantages too. It is not possible to calculate the mean for very large data as it would be time consuming to do so. We should also consider that the extreme values in the observations may lead to calculation errors and so also the percentages and ratios and we may not get a correct interpretation of the given data. We should remember the basic formulas to be used to calculate mean.