Just like every other topic in maths, students often have this general misconception about averages and what it is really about. This also affected me a student learning the art of solving maths problems, but I was able to jump out of it when I finally understood what it is all about.
The first thought that comes to one’s mind when the word “averages” is first mentioned is that has to do with finding the midpoint of certain things. But in the real sense of things, it is way more than that. Right here, I will be taking you through the types of averages that we have and their applications.
But before we proceed, let’s take a look at the general idea of what an average is. This understanding is what we will be building on as we proceed.
What are Averages
Taking a general look at it, an average is either a single character, number or symbol taking from a series of others, which acts as the general representative. This representative is supposed to posse a large number of the characteristics of the set of numbers, characters or symbols.
Averages are of different types. However, the major ones are mean, mode, median. These three gives clear definitions of what an average is all about. To further explain this, let’s take a look at what each of these is all about.
- Mean – This is often considered the average number from a given set of numbers. But in the real sense of things, it is way more than that. Mean is the total sum of all the numbers divided by the number of numbers. This type of average specifically states the center number from the given set of numbers.
- Mode – This simply refers to the most occurred number or character from a given set of numbers. It is often used to know which number occurred repeatedly the most. Which implies that the number has the highest probability of being the true value from the given set of numbers.
- Median – This type of average deals with the number at the center or middle of a given set of numbers. For this to hold, these set of numbers has to arrange in order of magnitude either ascending or in descending order.
Grouped Data
This is another major part of averages that needs understanding. Been able to get this right gave me an edge because not every question will come ungrouped. Often, numbers are given in a grouped manner. The good thing about grouped data is that they all revolve around the same formula with only slight differences. For example, to calculate the mean of a grouped data, the formula is simply ∑fx / ∑f, where f= frequency of the numbers, ∑ means the sum of, and x the midpoint of the group.
With this, you should be able to solve all kinds of averages problem. Moreover, Averages are a big part of the math sections of the SHSAT. You can prepare for the SHSAT at Caddell Prep if you need further assistance.
