- Level: AS and A Level
- Subject: Maths
- Word count: 3282
In this project I will be investigating three main hypotheses, which are all based on house prices.
Extracts from this document...
Introduction
Maths Coursework*
By Jo Kiddy
Introduction
In this project I will be investigating three main hypotheses, which are all based on house prices.
These hypotheses will include a number of statistical graphs and equations to acknowledge my understanding of how to interpret and how to represent the data collected.
I know that the price of the property increases within time and still increasing! Even though all areas have increased since 1960s and have increased hugely in the 80s even though the greatest of all increases is in 2003 this is because we have advanced tremendously since both periods. Mostly nowadays people living in England usually own their own houses and having to pay a mortgage each year.
This table shows the average price of all properties sold in the South West.
Average Sale Prices in South West - All Properties | ||||
Year | Jan-Mar | Apr-Jun | Jul-Sep | Oct-Dec |
1995 | £64 | £66 | £68 | £66 |
1996 | £64 | £67 | £71 | £70 |
1997 | £70 | £73 | £77 | £77 |
1998 | £77 | £81 | £84 | £82 |
1999 | £83 | £87 | £94 | £94 |
2000 | £97 | £103 | £109 | £109 |
2001 | £109 | £116 | £125 | £124 |
2002 | £126 | £138 | £152 |
This table shows the average price of all properties sold in the North East. |
Average Sale Prices in North East - All Properties | ||||
Year | Jan-Mar | Apr-Jun | Jul-Sep | Oct-Dec |
1995 | £48 | £50 | £50 | £49 |
1996 | £49 | £51 | £53 | £52 |
1997 | £53 | £54 | £66 | £57 |
1998 | £53 | £56 | £57 | £57 |
1999 | £56 | £59 | £61 | £61 |
2000 | £57 | £60 | £62 | £62 |
2001 | £61 | £64 | £69 | £68 |
2002 | £65 | £72 | £78 | £76 |
Price changes can be seasonal with the largest rises often occurring in the summer and the lower rises or even falling prices occurring in the winter. As each year passes by the more expensive the houses become. And the two tables show also that the South West is more expensive than the North East because of the situated area. A much more pleasant place to live, with mostly nice whether.
I am very aware that the figures are the actual asking prices for the properties and so therefore the actual price of the property will either be more or less then the asking
price.
Middle
3
£220
£250
£210
£265
£167
£165
£190
£190
£188
£190
£195
£150
£190
£250
£199
£205
£425
£187
£240
£340
£124
£210
£250
£176
4
£215
£270
£254
£300
£380
£265
£185
£250
£295
£260
£215
£260
£400
£318
£300
£480
£375
£510
£370
5
£410
£370
£395
£450
£400
£255
£356
£360
£398
£400
£490
£390
Here is all the data collected using the two samples mentioned on previous page and also put into a table.
Number of Bedrooms. | Total cost of all properties. | Average cost of all properties. |
1 | 1964 | 123% |
2 | 4918 | 154% |
3 | 4943 | 206% |
4 | 6324 | 264% |
5 | 6409 | 401% |
Now that I have sampled my data, I have put it into a simple table showing the total cost of all properties with no. Of bedrooms, and the average cost of all properties. I will now put the data collected into a scatter gram, with a line of best fit, the equation of a line of best fit, spearman’s rank correlation coefficient, and a bar chart.
By adding these statistical graphs and equations I should get an accurate result agreeing with my hypothesis.
Because my scatter diagram shows a moderate positive causality (Implies a direct link between two variables. One variable causes the change in the other variable.)
I am able to draw a line of best fit. The line of best fit will pass through the mean average of each data set.
You can see that as the number of bedrooms increase so does the price of that property. This means that there is a moderate positive causality.
First of all I need to find the mean of each variable.
Mean number of bedrooms. = 1 + 2 + 3 + 4 + 5
5
= 15
- = 3
Mean average price of all properties in %. = 123 + 154 + 206 + 264 + 401
= 1148
5 = 229.6 and I have rounded it up to 230
Now I will plot it on my graph with a cross and have the circle around the cross and also labelling it M so I know it’s the mean. After plotting the mean I am able to draw a line of best fit making sure that the line of best fit goes directly through the middle of the mean and as closely as possible to the points trying to have half of the points above and half the points below the line.
I am aware that using the line of best fit I can estimate other values from the graph.
This is called either interpolation or extrapolation.
Interpolation is an estimate from within the range of given x-values.
Extrapolation is an estimate from outside the range of given x-values.
170 are an estimate of the average price of all properties with a 2-bedroom house in (%). (This is an interpolation.)
The value 6 lies outside of the range of plotted points and so I needed to extend the line of best fit. 190 are an estimate of the average price of all properties with a 6-bedroom house in (%). (This is an extrapolation.)
When extrapolating data I should always question myself if the answer is realistic.
The further I extrapolate, the less reliable the estimate is.
The equation of a line of best fit.
Finding the line of best fit is exactly the same as finding the equation of any straight line.
I can calculate the equation of a line by equating gradients at two places.
The equation of a straight line is Y = MX + C.
To find the gradient, triangles are constructed on the line of best fit at two different places.
X Y
Point 1 (3, 130)
Point 2 (1.625, 170)
M = Y2 – Y1170 – 130
X2 – X1 1.625 - 3
Y = 87X+C
Y = 130
X = 3
130 = 87x3+C
130 = 261+C
130 – 261 = C
C = 131
Y = MX+C
Y = 87X+131
Y = X +64
The gradient is 87. The Y-intercept is 64
When X = 83, Y = 83 + 64.
= 147
So the predicted average cost of all properties is £147 for a 2-bedroom house.
Spearman’s Rank Correlation Coefficient.
Bed | Rank Order | Average cost | Rank Order | Difference = D | Difference2 = D |
1 | 1 | 123 | 1 | 0 | O |
2 | 2 | 154 | 2 | 0 | O |
3 | 3 | 206 | 3 | 0 | O |
4 | 4 | 264 | 4 | 0 | O |
5 | 5 | 401 | 5 | 0 | O |
Conclusion
These are the two bar charts for the average price in South West and North East – Jul-Sep 2002. These bar charts will show which is the most popular type of house in both North and South.
I will now calculate the equation for comparative pie charts and draw the comparative pie charts.
I knew that the North is cheaper than the South but I did not know until I had drawn the comparative pie charts out that the North East average cost of all properties is slightly less than half of the average cost of all properties in the South West.
I am pleased with this discovery, as I have learnt something new.
Conclusion Conclusion
These are the results to the first hypothesis:
As the number of bedrooms increased so does the Average cost of all properties increase in cost.
The cost of the property also depends on many other factors that also increase the cost. Houses in a paticular area in
What is desirable define it that is the problem cos more or less subjective judgement, what is desirable to one person may not be desirable to another.
That is true that the south is more expensive than the north which possiblies implies that the south is more desirable than the north.
South 2bdrms = north with more bedrms 4 same price.
As you increase the number of bedrooms the cost of that property also increases within the same area.
What maybe desirable to one person may not be desirable to another. What is desirable is a subjective judgement.
South is more desirable than the north south = 2bedrms =north you can get a 3or4 bedrooms for the same amount of money.
This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.
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