How To Calculate Mean, Median, Mode, and Range
Measures of central tendencies are crucial parts of maths, being that they can be used in several ways such as data analysis and drawing inference and estimate from a set of data. These measures are numerous in number, but the most important of them all are mean, median, mode, and range.
Despite how simple and straightforward measures of central tendencies are, many students still find it very difficult to understand it and make use of it the right way. This is not because they aren’t smart, but majorly because they are not getting it right. I can say this because I was once in those shoes.
To make comprehending it easier for students who are also finding this quite difficult, I have prepared a quick lesson on how to calculate mean, median, mode, and range below. With this, students will be able to learn what they need to know about these important measures of central tendency.
How To Calculate Arithmetic Mean
This concept comes first amidst other types of measures of central tendency. It majorly has to do with the ratio between the summation of all the values to the actual number of the values. More so, mean can be subdivided into two distinct types which are simple arithmetic mean and weighted arithmetic mean.
Being the most common, simple arithmetic mean takes into consideration each of the values in a given set of data and attach a high level of importance to each. While in the case of weighted arithmetic mean, the importance attached to the value as a whole. The general formula of mean goes as thus; Mean = ∑X ÷ N where ∑X= Sum of all the individual values and N= Total number of values.
How To Calculate Median
When it comes to calculating the median of a given set of data of an individual series, the first step that should be taken before any other thing is to first arrange the set of data in either an ascending or descending order and then count the number of the given set of data, denoting it by N. After counting the value of N is either going to be either even or odd in number.
If the value of N is odd, the formula to use is N’th term =(N+1)/2. After simplification, the value of the N’th term will be the median of the given set of data.
How To Calculate Mode
Just like the measures of central tendencies discussed above, the model can also be separated into individual series or discrete series. For the individual series, it is simply the number that occurs more in a given set of data. In other words, it is the number which frequently occurs. On the other hand, Discrete Series considers the frequency of the given set of data. Here, the number with the highest frequency is referred to as the mode.
How To Calculate Range
The range is quite simple and straight forward. Here, we are simply to find the difference between the highest value of a given set of data. This is done by subtracting the lowest value from the highest value.
Solved Example: Given 13, 18, 13, 14, 13, 16, 14, 21, 13, find their mean, median, mode, and range.
From our understanding of mean (Mean = ∑X ÷ N) we can proceed to simply this as (13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9. From here, we will get 15 as the value of our mean.
To solve for mean, we will make use of N’th term =(N+1)/2, where the value of N= 9. By simplifying further, we will get (9 + 1) ÷ 2 = 10 ÷ 2 = 5th. This gives us 14 as our median.
From the explanation above, everyone would agree with me that our mode here is 13, the reason being that it occurs more often than every other number.
Lastly, our range is simply 21 – 13 = 8. Where 21 has the largest value, while 13 has the lowest value. Hence our range becomes 8.