VCE General & Further Maths Question Thread!

[abcdqdxD]

Can someone explain how to "comment on histograms" and "compare histograms A and B" ?

Cheers

[Zealous]

Can someone explain how to "comment on histograms" and "compare histograms A and B" ?

Cheers

I'm pretty sure you can comment on histograms just like you would comment on a boxplot or a bar chart.

You can look at the distribution, whether it is positively or negatively skewed (or approximately symmetric). You can look at the spread of the data, for example the data in A might be spread out and the data in B may be tightly bunched up, you can comment on that and say that the histogram A shows data with a greater spread, if you have actual statistic values you should probably mention them to back up your comments (IQR, Range, Median, Mean etc...)

Other things like median, mean, can also be taken into consideration.

[Yacoubb]

Can someone explain how to "comment on histograms" and "compare histograms A and B" ?

Cheers

So firstly, a histogram is a great way of displaying univariate, numerical data in a really economical way, when you have more than 40 data values. When looking at histograms, you can gather four summary statistic values:

(a) Shape
(b) Centre
(c) Spread - in terms of range.
(d) Outliers (if any)

Shape:
* The shape of the histogram can be:
- Positively skewed (median < mean)
- Negatively skewed (median > mean)
- Approximately symmetric (median = mean)

Outliers:
Outliers are data values that lie a significant distance away from the main body of data under analysis. You may or may not have any outliers in the data set.

For example: The distribution of 12 pre-schoolers' head circumferences is approximately symmetric, with no apparent outliers.

Centre:
The data distribution is centered at the median value.

You find this by calculating . Sometimes, in a data set you are given, your central point of tendency (i.e. median) will be found somewhere in a particular interval. This is usually the case with continuous, numerical data.

For example: The head circumferences of the preschoolers is centered somewhere in the interval 22 - 26cm, the median value.

Spread:
Usually, when we analyse a data set, we look at spread in terms of Range (Max - Min) and IQR (Q3 - Q1). However, because we don't have enough information given to us or displayed on a histogram, we only use the Range as a measure of spread.



For example: The spread of the distribution of preschoolers' head circumferences, as measured by the range, is 12cm (30 cm - 18 cm).

So, altogether:

The distribution of head circumferences of preschoolers is approximately symmetric, with no apparent outliers. The distribution of head circumferences is centered at somewhere in the interval 22-26cm, the median value. The spread of the head circumferences, as measured by the range, is 12cm (30cm - 18cm).

_________________________________________________________________________

I think we've established that. Comparing two histograms is also easy

The distribution of head circumferences of preschooler boys is approximately symmetric with no apparent outliers, while the distribution of head circumferences of preeschooler girls is positively skewed with no outliers. The distribution of male preeschoolers' head circumferences is centered at a higher value than the distribution of female preschoolers' head circumferences, 25cm to 20cm, respectively. The spread of the distribution of male preschoolers' head circumferences, as measured by the range, is greater than that of spread of the distribution of female preschoolers' head circumferences, 12cm (30 - 18) to 8 cm (27-17) respectively. Overall, the head circumferences of males tend to be greater and more variable than females' head circumferences in the distribution.

[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.

Bump! I need help.

[Zealous]

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.
Bump! I need help.

Here's my working for your questions, have the picture by your side so you know all of the angles and the side lengths that I am referring to.

Q8B, you can use the cos rule to find BD, which is 7.32633

Then use DB, the angle BCD (88 degrees) and BC to find BDC using the sine rule.







Since we know two angles inside of the triangle BCD, we can find the angle DBC.





Then use the sin rule to find CD.








_________________________________________________________________________


For Q10b.
Use the cos rule to find AB, which was 10a, AB is 87.6071.

So CB will be 43.8036, which is half of it.

Now we can find angle QBA using the transposed cos rule with 3 sides, (this angle is the same as QBC).



In this context it is like:

where BA etc. are sidelengths.





After finding QBA, which is the same angle as QBC, you can then use the cos rule with QB and BC to find CQ.








edits: fixing messy working

[jeanweasley]

Here's my working for your questions, have the picture by your side so you know all of the angles and the side lengths that I am referring to.



edits: fixing messy working

Wow. Thanks for your help. Now I know why I got it wrong. I kept thinking of it as a right angle! Hahah. Thanks again. I won't get this question wrong EVER.

[abcdqdxD]

Thanks Yacouub. Will there be different expectations if the question asked to describe a boxplot? (Besides the fact that a BP provdes 5 simmaru statistics)

[Yacoubb]

Thanks Yacouub. Will there be different expectations if the question asked to describe a boxplot? (Besides the fact that a BP provdes 5 simmaru statistics)

You'd be required to quote the IQR (Q3-Q1). Other than that, you wouldn't be required to state anything else.

Remember, IQR = a measure of the spread of data around the median (central) point.

[abcdqdxD]

Hmm, what about if I'm asked to compare two distributions? How would you structure your response to make it time efficient (but still get the marks)?

[johnsmith123]

Hello,
Just looking for some help with these questions, for the one which isnt finished the question something like show why they chose the right option by choosing the variable loan through comparing interest.
I can do parts of both questions but i cant get the correct final answer for all parts. Thanks.

[johnsmith123]

 
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[johnsmith123]

Also this question i know its easy i just cant work out what im doing wrong.

[tcstudent]

hi all, im in search of a further math study guide on matrices, ive searched in the notes section of the forum but there is nothing on it, i understand it it an easy section for some, but couple of bits are hard. thank you

[jeanweasley]

hi all, im in search of a further math study guide on matrices, ive searched in the notes section of the forum but there is nothing on it, i understand it it an easy section for some, but couple of bits are hard. thank you

Here, this might be helpful

Edit: oops. Forgot the link http://www.sparknotes.com/math/algebra2/matrices/section1.rhtml

[tcstudent]

hello, cant wait to ask to my teacher so just going to ask here hehe, matrices module 6
question is

RS=T

s= 2   4         t= 0  2          find matrix r, cant find it in my book either
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