Question

What are the 3 types of averages?

Answer 1

Hint: We first explain the three types of averages - mean, median and mode. We explain the details and express them in general form of discrete data which can be used for the same process in continuous data. Then we use an example to understand the concept better.

Complete answer:
There are three types of averages. They are mean, median and mode.
Sample mean can be expressed as $\overline{x}=\dfrac{\sum{{{x}_{i}}}}{n}$ for inputs as ${{x}_{i}},i=1(1)n$.
In case of discrete data, the Median is the number in an ordered series midway between the range extremes.
We arrange the values and find the middle value of them. For a set of only two values, the median will be the same as the mean, or arithmetic average.
In general case we have to rearrange the numbers in order of lowest to highest.
When there are an odd number of values, we can just find the value so that there are the same number of values above as there are below this middle value. When there is an even number of values, there is an issue if there is not one number that acts as a middle value. Instead, the two middle numbers such that there are the same number of values above as below these two middle numbers. As a compromise, we take the average of these two middle numbers.
Mode is the value with the maximum frequency. Therefore, to find the mode for a given discrete value, we need to find the digit which has been used the greatest number of times i.e., the greatest number of frequencies.
If there are more than one such number then we need to find the greatest number of those numbers as a mode.
We take an example of 11 discrete data $18,19,34,38,24,18,22,51,44,14,29$ and we need to find their mean, median and mode. In this sample $n=11$.
Arranging them in ascending order we get $14,18,18,19,22,24,29,34,38,44,51$. We consider the inputs as ${{x}_{i}},i=1(1)11$.
Sample mean can be expressed as $\overline{x}=\dfrac{\sum{{{x}_{i}}}}{n}$. Putting the values, we get
\[\overline{x}=\dfrac{14+18+18+19+22+24+29+34+38+44+51}{11}=\dfrac{311}{11}=28.28\].
Sample median is expressed as the middle point of the ordered sample either in ascending or descending order. In this case of $14,18,18,19,22,24,29,34,38,44,51$, the median is 24.
The mode will be the 18 as it is in the sample twice and all the rest are distinct.

Note:
The mode can be the same value as the mean and/or median, but this is usually not the case. The mode is not affected by extreme values. The mode can be computed in an open-ended frequency table.