average savings

Average: Consecutive Savings Plan

Isn’t Average an Easy topic?

Here’s a tricky P5 question on Average. On the surface it, it looks quite easy because there aren’t a lot of numbers or diagrams, and the question is rather short. However, upon trying it out, students may find themselves in a very lengthy process of finding the answer. 😈
 
Most questions about Average tend to get very standardised and easy. In fact, in most assessment books, it’s one of the shorter chapters being covered.
However, the truth is far from it because Average can get very varied and tricky as it can tie in many other heuristics. It also boarders on the abstract, so educators will typically not use any form of visualisation to explain to Average to students. Thus, this often leave students in the Visual/Spatial category stranded. 😣
 
As in the question stated here, it seems all the student needs to do is to find out how many weeks there are in a year, then add $2 to every consecutive week, get the total and divide the total by the number of weeks. That is until the student finds out that there are 52 weeks to keep adding $2 to, and then to add all the values for the 52 weeks together!
 
This problem can be solved very easily if we break it down into different heuristics.
The steps and answer are below.

Steps:

1. Student needs to know that there are 365 days in a year. It doesn’t matter if it is a leap year because the number of weeks will still stay the same.
365÷7 ≈ 52
 
2. At this point, the student can get the total using the (a)Gaussian method or the answer using(b) Consecutive Average method.
 
(a)Using Gaussian method:
Last term’s value = (52-1)x2 + 2=104
2+104=106 (Value of each pair)
(52×106)÷2=2703
average = 2703÷52 = 53
Answer: $53 per week
 
(b)Using the Consecutive Average method:
Last term’s value = (52-1)x2 + 2=104
Average = (2+104)÷2 = 53
Answer: $53 per week 😎 👍🏻
 

Final thoughts:

In conclusion, this question can actually be solved in about 3 to 6 steps. This is one of the many heuristics that will be covered in our online portal when it is completed.
 
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