3 Key Terms in Statistics: Mean, Median, and Mode.
If you want to learn about statistics, you need to know three key terms: mean, median and mode. While each of these has its own specific mathematical definition, they’re often used in everyday speech as synonyms for average. Below, we’ll explore each of these terms in detail so you have a better idea of how each one plays into the bigger picture of statistics and math in general. We’ll also take a look at when it makes sense to use mean versus median or mode.
What is Mean?
Mean is a statistical term which is defined as the average of all the values in a data set. There are several types of mean, including the Arithmetic Mean, Weighted Mean, and Geometric Mean.
The Arithmetic Mean is the most common type of mean and is calculated by taking the sum of all the values in the data set and dividing it by the number of values. This type of mean is used to measure central tendency when dealing with numerical data. Arithmetic mean of finite set x_1,x_2,x_3…….x_n is denoted by x bar”.
Let's pick an example to calculate the mean of this data set x = [1, 4, 2, 5, 2, 2, 9].
The mean of this data set is 3.57.
Mean has a property that it is easily biased by outlier in the data set(Skweuad data). So when we calculate the Central tendency of data “mean” is not the only thing that we should consider.
let’s find out how the mean is biased by outliers in data. For this, we add an extra data point in our previous data set. x = [1, 4, 2, 5, 2, 2, 9, 15]
Here by adding only 15 to the data set x mean is shifted from 3.57 to 5. This is very misleading when only mean is considered to interpret the data in statistics.
A fun fact about mean is that it was first described by Aristotle in his treatise Metaphysics. He wrote that the mean is that by which the extremes are joined together and described it as an intermediate between two extremes.
What is the Median?
In statistics, the median of a data set is the middle value. The middle value is, half of the points are below the median and the other half is above the median. The Median is not biased by extremely low or high values(outliers) as the mean gets biased. To calculate the median of the data set we sort the data in either ascending or descending order first. There are two formulas to calculate median -
- If the length of the data set is even -
- If the length of the data set is odd -
Where n is the length of the data set.
We will take the same data set x = [$1,4,2,5,2, 2,9$] to calculate the median. First, we have to rearrange the data set in ascending or descending order, For now, I am rearranging the data in ascending order. Which looks like this x = [$1,2,2,2,4,5,9$].
The Median is 2 for this data set. which is different from the mean.
What is the mode?
Mode is a key term in statistics that measures the most frequently occurring value in a data set. It can be used to identify which items are the most popular or common in a certain set of data. A mode is an important tool for quickly understanding trends in data. It’s important to note that there may be multiple modes if more than one number has the same highest count.
For our data set x = [1, 4, 2, 5, 2, 2, 9] mode is 2 which has the highest count of 3.
Fun fact: Mode is the only measure of central tendency that can be used with categorical data! This type of data doesn’t involve numbers but instead uses categories like hair colour or music genre to group similar items together. No matter the type of data you’re analyzing, understanding mode is a key part of understanding math.
Conclusion
In conclusion, Mean, Median and Mode are three of the most important terms in Statistics. They each refer to different ways of measuring a set of numbers, providing valuable insights into the underlying data. Mean is the average value of all the numbers in the set. The Median is the middle value of the set when all the numbers are sorted in numerical order. Mode is the most common number among the set. All three of these measures are useful when trying to understand data, make predictions and draw conclusions. Math is an essential tool for calculating each of these values, so having a good understanding of basic mathematical operations is key when working with mean, median and mode.
