VCE Further Maths Exam 1 Discussion and Solutions

[dec.hargreaves]

It's probably been such a big problem because seasonal indices are usually seen to be used for sales in a season (month, year, quarter), and having a negative seasonal index means you have had negative amount of sales

[Educator]

True, most of the Exam and textbook examples deal with positive numbers such as sales, but it's easy enough to think of examples with negative raw data such as average temperatures in Antarctica: (I made these numbers up)

Winter: -20 degrees
Spring: -5 degrees
Summer: 10 degrees
Autumn: 5 degrees

[addictwithatextbook]

Okay, so it wasn't just me thinking so. I was panicking in the latter half of the exam when I realised seasonal indices COULD be negative through example calculations, and spent most of the final minutes doubting myself and wondering if a moving mean in a smoothed time series could be negative. I just chose D because I thought it would be the likely answer the majority of students would choose. Thanks, Educator.

[Educator]

D is the best and most logical answer, but not clear cut.
The textbook method for calculating SI's can lead to negative SI's.

[Paolo Grande]

Think about what a seasonal index is. Its a comparison to the seasonal average. This means that in relation to the seasonal average a value of an index can either be below or above one. If a value is 1.6 then we have a situation where the seasonal index indicates 60% above the seasonal average. A seasonal index of 0.65 tells us that that season is 35% below the seasonal average. A negative seasonal index does not make sense as it can't be compared to seasonal average of 1.
The other point is that when looking at  amounts in relation to time, negative values do not make sense so consequently negative seasonal indices are not possible.
All the other options can definitely be negative so D is the correct answer. The  VCAA would not be so sloppy in such a question to make an error.

[Steve252]

It seems to me that a negative seasonal index theoretically makes sense.
If a seasonal index of 1.6 means 60% above the average, in the same way, a seasonal index of -0.5 would mean it is 150% below the average, as in 1.5 times below the average

[Mattjbr2]

Can we please discuss why question 13 is not C? To me it looks like there's a pattern that repeats every ~7 days. Must seasonality have perfectly equal width between every single crest and trough? I thought it can be approximately the same each time give or take 1 day, hence why i assumed it's seasonal with some random fuzziness in places, i.e. random fluctuations. How can you confidently, with 100% certainty, say it's B? See the attached image for my thought process.

[jonwil]

Can we please discuss why question 13 is not C? To me it looks like there's a pattern that repeats every ~7 days. Must seasonality have perfectly equal width between every single crest and trough? I thought it can be approximately the same each time give or take 1 day, hence why i assumed it's seasonal with some random fuzziness in places, i.e. random fluctuations. How can you confidently, with 100% certainty, say it's B? See the attached image for my thought process.

Cos your high points aren't consistent
They come at 7, 12, 20 which aren't consistent enough to argue for seasonality.
Even the low points bro
1,2  10, 15, 19
Whatever 3 points you decide to choose you can't really make a relation out of it.
So yeah
100% B
The only thing is a possible increase but nothing really shows it so B