VCE General & Further Maths Question Thread!

[Yacoubb]

You'd only centre the data during (even number)-pt moving mean smoothing such as 2-pt, 4pt etc.
This is because when you initially find the mean, the centre of the points is not actually belonging to the original series (or original time value). We then have to 'centre' the means through finding the 2-pt moving mean again of the already smoothed values in order to allow them to line up with their original time values.
This is would be better demonstrated using a visualised table, so perhaps try drawing one out!

However, in your case of a 5-pt moving mean or any (odd number)-pt moving mean, centring would definitely not be required. Perhaps it was a trick or a typo in the question that was provided to you so don't stress!

Hope I helped

That's right. Only when you have to smooth an even number of points (i.e. you perform smoothing WITH centring for 2-moving mean and 4-moving mean. Its usually always displayed in tabular form

[Professor Polonsky]

As far as I can tell, most people seem to have already finished core. Have you guys also done a module, or did you start with core?

[brenden]

My guys have done a SAC for Matrices, and done a SAC for everything in Core except for Time Series... they're doing the Time Series SAC soon though.

[Patches]

We did a geometry SAC, and now we're about halfway through the core.

[jeanweasley]

I'm having a SAC on time series soon but there's one thing bugging me.
I find it hard to differentiate between seasonal and seasonal with trend. For example, if you're given a graph and you see that there are peaks and troughs, how do you determine if it is indeed seasonal only and not with trend or the other way around?

[aestheticatar]

I'm having a SAC on time series soon but there's one thing bugging me.
I find it hard to differentiate between seasonal and seasonal with trend. For example, if you're given a graph and you see that there are peaks and troughs, how do you determine if it is indeed seasonal only and not with trend or the other way around?

You can identify a seasonal variation within in your time series data through observing its predictable and repetitive fluctuating movements.

Time series data that contain a trend have a clear overall increase or decrease over the significant period of time.

Hence a time series data with both a seasonal and trend pattern will have predictable and repetitive fluctuating movements as well as a clear overall increase or decrease over the period of time.
(Value at start of season tends to be significanly higher or lower compared to value at end of season)

Time series data with seasonal variation only will have predictable and repetitive fluctuating movements but no clear overall increase or decrease over the period of time.
(Value at start of season tends to be similar to value at end of season)

Hope I helped

[Yacoubb]

I'm having a SAC on time series soon but there's one thing bugging me.
I find it hard to differentiate between seasonal and seasonal with trend. For example, if you're given a graph and you see that there are peaks and troughs, how do you determine if it is indeed seasonal only and not with trend or the other way around?

Okay so the first thing you need to understand is that when you're analysing a time series plot, there are two main features:
(a) Trend - increasing (upward) or decreasing downward
(b) Variation - seasonal (pattern), cyclical (pattern) or random.

Seasonal variation can easily be identified by looking at a period of one year or less and observing evidently regular fluctuations (i.e. troughs and peaks occur at consistent time intervals over the time frame under analysis.

Now its one thing to identify seasonal variation, and another to determine trend. I had a TIME SERIES SAC today and my time series plot showed a decreasing (downward) trend with seasonal variation. Just note that in order to calculate seasonal indices, you MUST have a seasonal component (i.e. seasonal variation). Just a tip if you're stuck with what type of variation you've got.

Trend can be identified two ways. Firstly, sometimes its extremely easy to see a visible trend simply by looking at the graph, usually if you have a fair few plotted points (i.e. 8 points +). However, sometimes you have insufficient points to see any visible trend, and a tip would be to simply use your calculator to find the regression line of your time series plot; if the gradient/slope is (+), you're looking at an increasing trend, and (-) slope/gradient corresponds to a decreasing downward trend. Sometimes, there is no trend. It is possible to have seasonal variation with NO trend (i.e. over many years, you're having consistency in the seasonal component and the DV does not decrease/increase over the timeframe).

If there is a trend, you can use your rule to see a visible trend simply by looking at the overall trend of the graph, or as mentioned, using your calculator. But if no trend is visible, you practically see that there is no increase/decrease in DV over the timeframe. You can also look at the raw data; if the values of the data decrease over the quarters/months/terms, etc, there is probably going to be a decreasing (downward) trend.

Hope this helped, and best of luck!

[jeanweasley]

Okay so the first thing you need to understand is that when you're analysing a time series plot, there are two main features:
(a) Trend - increasing (upward) or decreasing downward
(b) Variation - seasonal (pattern), cyclical (pattern) or random.

Seasonal variation can easily be identified by looking at a period of one year or less and observing evidently regular fluctuations (i.e. troughs and peaks occur at consistent time intervals over the time frame under analysis.

Now its one thing to identify seasonal variation, and another to determine trend. I had a TIME SERIES SAC today and my time series plot showed a decreasing (downward) trend with seasonal variation. Just note that in order to calculate seasonal indices, you MUST have a seasonal component (i.e. seasonal variation). Just a tip if you're stuck with what type of variation you've got.

Trend can be identified two ways. Firstly, sometimes its extremely easy to see a visible trend simply by looking at the graph, usually if you have a fair few plotted points (i.e. 8 points +). However, sometimes you have insufficient points to see any visible trend, and a tip would be to simply use your calculator to find the regression line of your time series plot; if the gradient/slope is (+), you're looking at an increasing trend, and (-) slope/gradient corresponds to a decreasing downward trend. Sometimes, there is no trend. It is possible to have seasonal variation with NO trend (i.e. over many years, you're having consistency in the seasonal component and the DV does not decrease/increase over the timeframe).

If there is a trend, you can use your rule to see a visible trend simply by looking at the overall trend of the graph, or as mentioned, using your calculator. But if no trend is visible, you practically see that there is no increase/decrease in DV over the timeframe. You can also look at the raw data; if the values of the data decrease over the quarters/months/terms, etc, there is probably going to be a decreasing (downward) trend.

Hope this helped, and best of luck!

Thank you. That was indeed helpful.

[Yacoubb]

As far as I can tell, most people seem to have already finished core. Have you guys also done a module, or did you start with core?

We finished the Core: Data Analysis and we'll be staring Module One: Number Patterns next week. I think the plan is to finish everything by mid term 3; the remainder of the time will be devoted to revision for the exams.

Upcoming Number Patterns SAC will probably be in about a month from now; my teacher wants to devote a lot of time to the modules!

[Professor Polonsky]

We've finished a module already, and just finished Chapter 3 of Maths Quest. Our SAC on data analysis is only in like 5-6 weeks, though.

[jeanweasley]

Just finished the time series SAC. I think I did pretty well. Thanks for your help Yacoubb.

We're now starting on Trig.

[Yacoubb]

Just finished the time series SAC. I think I did pretty well. Thanks for your help Yacoubb.

We're now starting on Trig.

Glad to hear We're starting on Number Patterns, a weird module lol!

[Coopermoody]

Does anyone have a technique for these type of questions?

[vashappenin]

Can someone please explain Fibonacci Sequences to me?? I'm sooo confused with how to do them on the calculator :S

[jeanweasley]

Hey, I am really stuck on Question 8 and 10. I answered 8a fine and got it right but 8b doesn't make sense to me. I keep getting 5.99 and the answer is 5.53 cm.
As for Question 10, I got 10a right too but I'm also having trouble with the second part to the question.
The answer to 10b is 67.7 cm.

http://cambridge.edu.au/go/interactive_book/books/vce_further_maths/images/chapter/inline-405.gif  <-- The questions are there. 8 and 10.