This method of sampling is a very time consuming so therefore I will go back and just do a simple random sample. I’ve realised that it’s possible to do a convenience sample in which I choose the first few pages of a property page and take all the property prices from those pages until I have the sample needed which is about 100.
The source of data that I have collected is secondary and primary this is because even though I have collected the data specified I did collect this specified data from property advertisers (which is second hand information.
Here is all the data collected using the two samples mentioned on previous page and also put into a table.
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 – Y1 170 – 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.
= 0 N = 5
SR = 1- 6
n(n –1)
= 1- 6x0
5(25-1) = 0
= 1 – 0 = 1
Strong positive causality this agrees with my hypothesis that as one increases so does the other.
Hypothesis
“ The price of a property depends on how desirable people who want to buy the houses think the area is.”
My choice on wanting to do this hypothesis is to understand where is the best possible place to buy a house. This is why I have decided to collect data from three local areas and see how each one compares to one another, how much the property will cost, and whether the area has a bad reputation. All these factors I have put into consideration, as every family wants the best they can afford and manage.
I have done a random sample by putting 10 areas into a hat and asking a member of my family to pick 3. Those 3 that were picked were Sandbanks, Queens Park and Corfe Mullen.
This table shows
The data has been sampled and now able to be put into a much simpler table only showing the areas, the total cost of all properties with 3-bedrooms, and the average cost of all properties. I will now put the data collected into a cumulative frequency polygon with the median and quartiles, also the three types of averages that are the arithmetic mean, median, and mode. A box and whisker diagram, a bar chart or two, pie chart, comparative pie charts.
By adding these statistical graphs and equations I should get an accurate result agreeing with my hypothesis.
I have done a simple random sample of about 20 for each area that is mentioned above. And calculated the total and have calculated the average as shown below in the table. With the Average cost of all properties with a 3-bedroom house that is situated in Sandbanks the total average is too high so in the bar graph, the pie chart and in other statistical graphs and equations I have written 1000. Both of the charts still show that Sandbanks is way up they’re in the lead but with a price that is more realistic for the amount of data that I have and will use.
This pie chart show that the houses in Sandbanks are very expensive this is because of many factors such as the location, quality of the house, a number of facilities the house includes e.g. garage, garden size of the rooms etc.
Most of the houses that are situated in Sandbanks are highly over priced but if you want a view looking onto the sea that is what is expected from you. In contrast Corfe Mullen has not got a pleasant view such as the sea but is more situated closer inland making the houses in this area less expensive. The quality of the house, the location, and a number of facilities also helps in the final price of the property. Whereas in Queens Park an area which is not unpleasant but nor near the seaside has quite highly priced properties, this is also because of the quality of the house, the number of facilities, and also it is situated pretty close to Bournemouth.
The bar chart below also shows the same as the pie chart.
I am very happy with the results from both graphs they both indicate that the price of a property depends on how desirable people who want to buy the houses think the area
I will now draw a outdoor bar chart as I want to compare totals, and I believe using this bar chart will help me see the total much more easily. This bar chart is like the same above but it is much clearer to understand as it shows and tells you exactly how much the average cost is of these 3 different areas.
Comparative Pie Charts
I will now draw a comparative pie chart as I can use these pie charts to display two or more sets of data. To do this accurately I must ensure that the areas of the circle are in the same proportion as the totals displayed on each chart.
The workings out are on the next page the result of the workings out tell me exactly what I thought would happen in which the price of a property depends on how desirable people who want to buy the houses think the area is. Also showing that Sandbanks is the most expensive area followed by Queens Park and last of all Corfe Mullen.
Hypothesis
“House prices will tend to be higher in the south than in the north.”
I have decided to investigate this hypothesis as even though houses in the north are the same price in the south you can get a much bigger house up there than down here e.g. an 2 bedroom flat/apartment could be a 3 or 4 bedroom house in the north for the same amount of money. I just want to confirm my hypothesis with information to back me up. This is why I have decided to collect data from 2 areas one in the South West and the other area in the North East and see how each one compares to one another.
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.
Now that I have sampled my data, I have put it into a simple table showing the total cost of all properties within specific months and the years in which the properties prices has increased (Above).
I will now put the data collected into many types of bar charts, Comparative pie charts, pie charts, averages.
By adding these statistical graphs and equations I should get an accurate result agreeing with my hypothesis.
I will inter-relate my three hypotheses with one another, as they all relate with house prices. What affects the price of the property, the location, the number of bedrooms, and whether the properties are situated in the North or South of England.
The source of data that I have collected is secondary this is because I have collected this specified data from the Internet (which is second hand information).
I don’t think I have used any type of sampling but then I have used a convenience sample without knowing I did so I think I did this by typing in house prices in Google search engine in which I choose the first few Internet sites that came up and I took as much information from those sites as possible to ensure I had enough data to create statistical graphs from the data collected.
Both Bar graphs show the price increase each year in the south West and in the North East and as you can see there is a slight difference in which the South West has a higher percentage increase than in the North East.
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.
