My question is specifically regarding Q24 (as show in the screenshot). The question refers to the graph on the left hand side and it asks to find per year average number of miles flown from 1965 to 1970. I understood the question pretty well and found the answer by adding up all the values from the year 1965 to 1970 and then dividing that by 6 but my question is, in one of the big book solutions videos, Greg also says that you have to be careful with these average questions as sometimes you might just need to add first and last to get the average so i wanted to understand how can we differentiate between such questions and understand what kind of average is question referring to?
I think my question was a little vague and unclear, I was referring to some specific wording that such questions use to ask average and I am unable to find the exact video where Greg says that so if I come across any such situation I will share that on this thread but your answer about linearity definitely makes sense. Thank you for replying!
I wanted to follow up on this because I’ve identified the exact question I wanted to ask. In the two questions, you’ll notice that for the one from the big book, we find the average decline in student population from 1972 to 1980 by taking the absolute difference between the populations and dividing it by the number of years in that period. However, for the other question, when I attempted a similar approach to calculate the percentage increase from 1935 to 1960—dividing that increase by how many groups of five-year periods we have—I found an incorrect answer. My initial method was to calculate the percentage increase from 1935 to 1960 and then divide it by 5. The correct solution involved finding each individual percentage increase for each five-year period and then averaging those increases by dividing their total sum by 5. I’m confused as to why we can’t apply consistent logic here since even in the big book question, this increase wasn’t linear and varied across periods. Why does it differ in this case?
I want to ensure that I am not just memorizing this, but truly understanding the reasoning behind it. I would appreciate it if you could explain the concept to me. Thank you!
