Question

If a person scores in the ${{45}^{th}}$ percentile on the ACT, then how do we interpret this?

Answer 1

Hint: We can interpret the person’s capacity among the people that participated in that respective ACT. The term ${{45}^{th}}$ percentile represents the percentage or else the position of that respected person among all the people scored in that ACT.
We need to use the definition of percentage to interpret the data given. Generally, $x%$ score is nothing but getting $'x'$ marks for 100 marks.

Complete step by step answer:
We are given that a person scored ${{45}^{th}}$ percentile on the ACT.
Let us assume that the person be some $'X'$
We know that the general understanding of percentage is $x\%$ score is nothing but getting $'x'$ marks for 100 marks.
Now, let us apply the same theory for the given data also assuming there are a total of 100 people participating in the ACT.
Here, we can see that the person $'X'$ is in the position of 45 for taking 100 people that participated in the ACT.
Here, we can also state that there are 55 people good compared to $X$ in that 100 people.
Here, we can see that we can understand the position of $X$ for 100 people. But, if we consider the whole number of people that participated in the act then we can say that there are nearly 55% of the participated people that are good compared to $X$
Also, we can state that there are 44% of people participated in the ACT are not good when compared to $X$
Therefore, we can conclude that there are 55% of people that are good and 44% of people that are not good when compared to the person who got 45% in the ACT.

Note: We need to note that the percentage is always calculated to 100%. So, if we take the total quantity to 100 then the percentage given will represent the position of the given quantity.
But this is only assumption so that we need to generalise for the whole set of people or quantity in terms of percentages only at the end because the total quantity may or may not be equal to 100 and also there is possibility for less than or greater then 100 also. So, representing the interpretation in terms of percentages is the best way to interpret the data.