Statistics calculations and diagrams

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Year11guy
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#1
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#1
I'm on the calculations and diagrams stage of my CW for Statistics GCSE. It's out of 12 and I'd like to get 10 marks minimum
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Chlorophile
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#2
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(Original post by Year11guy)
I'm on the calculations and diagrams stage of my CW for Statistics GCSE. It's out of 12 and I'd like to get 10 marks minimum
What's your question?
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Year11guy
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#3
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(Original post by Chlorophile)
What's your question?
Oh sorry didn't realise. I wanted to know whether I'm supposed to interpret my graphs at this stage or wait until the next one, I mean like writing whether or not the calculations support my hypothesis. Also, anything I can include to get the top marks would be useful.
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Year11guy
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Any help?
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Chlorophile
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(Original post by Year11guy)
Oh sorry didn't realise. I wanted to know whether I'm supposed to interpret my graphs at this stage or wait until the next one, I mean like writing whether or not the calculations support my hypothesis. Also, anything I can include to get the top marks would be useful.
I honestly don't know, I didn't take statistics at GCSE. If there's anything specific you need help with I can see what I can do, but I don't know what you're being marked on in this coursework.
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Year11guy
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(Original post by Chlorophile)
I honestly don't know, I didn't take statistics at GCSE. If there's anything specific you need help with I can see what I can do, but I don't know what you're being marked on in this coursework.
If I'm trying to show distribution, what calculations should I use? I'm doing histograms so far
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Chlorophile
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#7
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(Original post by Year11guy)
If I'm trying to show distribution, what calculations should I use? I'm doing histograms so far
It depends on what you're showing a distribution of but yeah histograms are a sensible way of presenting a lot of distributions. In terms of calculations again it depends on what you're showing but you would probably want to have the mean, probably the three quartiles and possibly the mode. Standard deviation is definitely a good idea to show dispersion and a measure of skew would also be good if there is skew. You could also mention if your distribution fits any 'real' distributions, such as a uniform discrete distribution or the normal distribution.
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Year11guy
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(Original post by Chlorophile)
It depends on what you're showing a distribution of but yeah histograms are a sensible way of presenting a lot of distributions. In terms of calculations again it depends on what you're showing but you would probably want to have the mean, probably the three quartiles and possibly the mode. Standard deviation is definitely a good idea to show dispersion and a measure of skew would also be good if there is skew. You could also mention if your distribution fits any 'real' distributions, such as a uniform discrete distribution or the normal distribution.
But my next hypothese was:
The variation of diesel cars will be higher than petrol cars. That's what I was going to use Standard Deviation for. Would this not be appropriate?

Btw, Im calculating Frequency Density and have come out with 0.01 as a FD. Is it normal to be this low?
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Chlorophile
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#9
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(Original post by Year11guy)
But my next hypothese was:
The variation of diesel cars will be higher than petrol cars. That's what I was going to use Standard Deviation for. Would this not be appropriate?

Btw, Im calculating Frequency Density and have come out with 0.01 as a FD. Is it normal to be this low?
What do you mean by variation? The variation in what? Fuel efficiency? Maximum speed? It's quite important and so are the results you've got. If there is a clear peak at the mean and there isn't too much skew, then yes the standard deviation is suitable. If there isn't a clear peak or there are multiple peaks or the distribution appears to be uniform, the standard deviation isn't suitable.

And the frequency density is frequency over class width, so it depends on these. If you had a frequency of 1 and a class width of 100, then the FD would be 0.01
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Year11guy
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#10
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(Original post by Chlorophile)
What do you mean by variation? The variation in what? Fuel efficiency? Maximum speed? It's quite important and so are the results you've got. If there is a clear peak at the mean and there isn't too much skew, then yes the standard deviation is suitable. If there isn't a clear peak or there are multiple peaks or the distribution appears to be uniform, the standard deviation isn't suitable.

And the frequency density is frequency over class width, so it depends on these. If you had a frequency of 1 and a class width of 100, then the FD would be 0.01
Oh, sorry for not being clear, I meant variation in price. Do the class widths of a Histogram have to be the same because I'm having a hard time of making equal class widths. Also, if the histogram doesn't begin at 0, is it necessary to draw a little squiggly line like at the start?
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Chlorophile
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#11
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#11
(Original post by Year11guy)
Oh, sorry for not being clear, I meant variation in price. Do the class widths of a Histogram have to be the same because I'm having a hard time of making equal class widths. Also, if the histogram doesn't begin at 0, is it necessary to draw a little squiggly line like at the start?
The class widths do not have to be the same. That's the main advantage of a histogram. If all the class widths are the same, you've basically just got a bar chart.

In generally, it's not a good idea to do the squiggly line thing in a graph because it can disguise trends. With a histogram, it's generally fine for the x axis (classes) but I wouldn't do it for the y (frequency density).
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Year11guy
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(Original post by Chlorophile)
The class widths do not have to be the same. That's the main advantage of a histogram. If all the class widths are the same, you've basically just got a bar chart.

In generally, it's not a good idea to do the squiggly line thing in a graph because it can disguise trends. With a histogram, it's generally fine for the x axis (classes) but I wouldn't do it for the y (frequency density).
What about a box plot?
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Chlorophile
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#13
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(Original post by Year11guy)
What about a box plot?
You could do both. A box plot isn't as informative as a histogram so whilst you could have a box plot to supplement a histogram, I wouldn't replace a histogram with a box plot.
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Year11guy
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#14
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(Original post by Chlorophile)
You could do both. A box plot isn't as informative as a histogram so whilst you could have a box plot to supplement a histogram, I wouldn't replace a histogram with a box plot.
Yeah, that's what I meant, a box plot to support my histogram. My hypothesis is: Diesel cars have a wider distribution of prices than petrol cars. I will do a histogram for petrol and one for diesel cars. What should I look out for on my Histograms to prove/disprove my hypotheses?

Also, for my final hypotheses, a SD calculation will suffice?
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Chlorophile
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#15
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(Original post by Year11guy)
Yeah, that's what I meant, a box plot to support my histogram. My hypothesis is: Diesel cars have a wider distribution of prices than petrol cars. I will do a histogram for petrol and one for diesel cars. What should I look out for on my Histograms to prove/disprove my hypotheses?

Also, for my final hypotheses, a SD calculation will suffice?
So there are a number of different measures of variation. I suppose the main ones at your level are the standard deviation, the interquartile range and the total range. Give all three and justify their use and it should be fine.
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Year11guy
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#16
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(Original post by Chlorophile)
So there are a number of different measures of variation. I suppose the main ones at your level are the standard deviation, the interquartile range and the total range. Give all three and justify their use and it should be fine.
What should I look out for on my Histograms to prove/disprove my hypotheses?
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Chlorophile
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#17
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#17
(Original post by Year11guy)
What should I look out for on my Histograms to prove/disprove my hypotheses?
Basically, you're looking for a more 'spread out' shape. A histogram with a low variance will have a big central peak (or a couple of adjacent big central peaks) and everything else will be small. A histogram with high variance will only have a small central peak. Essentially, low variance is mountain shaped and high variance is hill shaped.

However, you shouldn't really be using the histograms to compare variance because they're made for representing data, not comparing variance. Box plots are much better at specifically showing variance because they really clearly show the IQR so direct comparisons are easier. And obviously, knowing the IQR and Stdev allow you to make quantitative comparisons.
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