VCE General & Further Maths Question Thread!

[brenden]

Yeah, I think so

[Stick]

Thanks,
There is a question that is 2 marks and asks us to comment on the features of the time series plot. Would saying that it has a positive/upward cyclic trend be enough for the 2 marks?

Two marks indicates that two pieces of information are required, so yes, you have fulfilled the criteria and mark allocation with that description.

[aestheticatar]

Hey what's up guys,

When analysing a percentage histogram and representing it with a box plot what's the best technique to use?
(For example, take a look at Q6 VCAA 2009 Exam 1)

Also, if a percentage histogram is bimodal, do the two 'modes' have to be exactly the same percentage/value? If not, how much variance may exist between the two until the histogram is no longer considered bimodal?

Thanks in advance!

[jimmy22]

Hey,
In what type of time series plots would it not be appropriate to use a least squares regression line?

I have a question that wants me to say if it is appropriate to use a least squares regression line is appropriate to model an increasing seasonal trend. I know that the answer would be no, but not sure how to explain (as it's 2 marks).

thanks

[Yacoubb]

Hey,
In what type of time series plots would it not be appropriate to use a least squares regression line?

I have a question that wants me to say if it is appropriate to use a least squares regression line is appropriate to model an increasing seasonal trend. I know that the answer would be no, but not sure how to explain (as it's 2 marks).

thanks

The more linear (or secular is good to use here) a trend is, the more appropriate it is to use the least squares regression line. The correlation between the time (IV) and the DV is very strong if it is linear.

So, if it is seasonal, you're looking at relatively large fluctuations, peaks and troughs, not displaying a strong correlation between IV and DV. Because least squares regression line assumes linearity and therefore a strong correlation, it would be inappropriate to use a linear model to describe the increasing trend between IV and DV.

[jimmy22]

Oh i see. Thank you very much.

Just another thing, apparently if a graph is approximately symmetrical the mean is a better measure of centre (than the median). Why is this so?

[jimmy22]

anyone?

[Daenerys Targaryen]

Don't know for sure but:

On a normal symmetrically distributed bell curve.
Such as the one for the 68-97% Rule (IDR the exact numbers. Awks)

But the middle section for the peak is x-bar (mean) So i guess that's why.

Don't know the exact mathematics behind it

[Yacoubb]

If a distribution is symmetric, you can use either the mean or median; this is because the mean is not affected if the distribution is symmetric with no outliers. This being the case, we can use either summary statistic.

[Stick]

I always went for the median because it works every time, regardless of the shape of the distribution.

[Yacoubb]

I always went for the median because it works every time, regardless of the shape of the distribution.

Yeah the median is always more reliabile.

[vashappenin]

Hey can someone please explain how to do:
- q13 from http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2009furmath1-w.pdf
- q9 from http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2008furmath1-w.pdf

Thanks!

[Zealous]

Hey can someone please explain how to do:
- q13 from http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2009furmath1-w.pdf
- q9 from http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2008furmath1-w.pdf

Thanks!

Hi,
For q13:
- Enter the data into lists and spreadsheets. Remember to let 1989 equal 1, 1990 equal 2. So your first column will have "1, 2, 3, 4"... and your second column will have the corresponding internet use percentages: "0.5, 0.6, 1.1, 1.8...."
- Perform a three median regression and find the "m" value or gradient value.

Spoiler

If your data is entered correctly, you should get a regression equation of

For q9:
- Enter the data for the weight of the fish into your calculator and find the median, so ignore the length of the fish as it is not being considered.

My answers:

Spoiler

I got D for q13 (0.45%) and C for Q9 (440g).

[memarani]

Upon observing the results with the 5-point smoothing, a trend appears. Take the data from the 5-point moving average smoothing and fit a straight line using the least-squares method. Put the first smoothed point at t = 3 and then centre the time data. State the y-intercept and gradient. Compare this trend line with that from question 3.

i'm confused on how to centre the time data or what is meant by that, can someone please explain this to me?

[aestheticatar]

Upon observing the results with the 5-point smoothing, a trend appears. Take the data from the 5-point moving average smoothing and fit a straight line using the least-squares method. Put the first smoothed point at t = 3 and then centre the time data. State the y-intercept and gradient. Compare this trend line with that from question 3.

i'm confused on how to centre the time data or what is meant by that, can someone please explain this to me?

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