CONDAMINE VS TOOGOOLAWAH Vince, Jordan Table of Contents 1.0 Introduction ....................................................................................................................................... 2 2.0 Methodology ..................................................................................................................................... 2 3.0 Hypothesis......................................................................................................................................... 3 4.0 Observations & assumptions ............................................................................................................. 3 5.0 Variables ........................................................................................................................................... 3 6.0 Data Summary .................................................................................................................................. 3 6.1.1 Original Data Summary Calculations – individual Data........................................................ 3 6.2 Grouped Data Summary Calculations........................................................................................... 4 7.0 Formulas, Calculations and Technology Used.................................................................................. 4 8.0 Findings............................................................................................................................................. 6 9.0 Reasonableness ................................................................................................................................. 6 10.0 Accuracy and validity ...................................................................................................................... 7 11.0 Limitations....................................................................................................................................... 7 12.0 appendix.......................................................................................................................................... 7 1.0 Introduction The purpose of this mathematical report is to investigate and compare house prices of two locations within Australia, Condamine and Toogoolawah. The aim is to find relevant and similar locations and determine whether there are any outliers or differences in prices in real estate. Similarities arise from the comparison of 2 bedrooms within the real estate search. 2.0 Methodology Data was collected from the website https://www.realestate.com.au/. The report will outline mean, median, range, quartiles, interquartile range, standard deviation with visual data representation in graphs. This also includes frequency tables, histograms and box and whisker plots to display spread/distribution of the two locations. All of the calculations were then done through using Microsoft excel. Such as mean, median, mode, range, interquartile range and standard deviation. Each and every statistic calculation was then manually checked and verified through the use of formulae. To then form data tables/sets allocated data minimised into smaller groups, big enough for a precise evaluation while using frequency tables, histograms and box whisker plots. The mathematical report will comprise on fluctuating levels of in-depth analysis to coincide with a proceeded conclusion regarding data allocated and analysed. Analysis will be done to a point to provide intuition into the current real estate market and determine discrimination in real estate prices in similar locations, Condamine and Toogoolawah. 3.0 Hypothesis The hypothesis formulated suggests that real estate prices from Condamine and Toogoolawah will consist of very similar mean, mode and median values, standard deviation and remaining calculations. 4.0 Observations & assumptions It is observed that the price range when observing all data points, there is a jump of prices within Toogoolawah prices in contrast to initial Condamine prices. All variation within the data points is dependent on whether the property size is different or including extras also. Extras seem to be a strong point for the variation in the data points An assumption that was made was that most if not all data points will be within a range of similarity. Considering all data points are sharing the trend of 2 bedrooms and 2 bathrooms, this assumption is excluding extras. Another assumption was that the first data points for Condamine might vary as some only have 1 bathroom unlike other data points. 5.0 Variables Variables used for data analysis were using an explicit number of fixed bedrooms, 2 bedrooms. Although the number of bathrooms could not stay fixed due to there not being enough data to keep all the points in the same variation. Considering this fact, the number of bedrooms was kept the same to provide a more appropriate spread within allocated data points. 6.0 Data Summary 6.1.1 Original Data Summary Calculations – individual Data location mean range median quartile 1 quartile 3 interquartile range (IQR) Standard deviation CONDAMINE 377,562 305,000 299,999 TOOGOOLAWAH 423,062 355,000 365,500 395,000 430,000 130,001 424,999 58,999 86,150 88,007 366,000 6.2 Grouped Data Summary Calculations 12 10 8 6 4 2 0 0 - 100,000 200,000 300,000 300,000 400,000 400,000 500,000 condamine 500,000 600,000 600,000 700,000 700,000 800,000 toogoolawah The data calculations proceeded to vary from mean to standard deviation, slightly configured new data set was considered. Although forming another data set would be unnecessary as original data set is pristine for calculations on its own. Through further examination it can be seen in the diagram that the data displays a positive skewness. Positive skewness can be depicted as the tail of distribution curve is longer on the right side. A box and whisker plot were constructed to show an extra level of skewness in the data. As seen in the box and whisker plot above, it excludes the outlier data to represent the viable data points allocated. See appendix for box plot including outlier. 7.0 Formulas, Calculations and Technology Used Toogoolawah data set calculations: Q1 : 370,500 Q3 : 417,499.5 IQR = 46,999 Mode : 395,000 Median : 395,000 Count (N): 16 Sum Σx: 6,768,995 Mean x̄: 423,062.1875 Variance s2: 7,745,388,275.2292 Standard Deviation s: 88,007.887573951 Standard deviation steps: Σ (xi - x̄)2 N-1 (345000 - 423062.1875)2 + ... + (700000 - 423062.1875)2 = 16 - 1 116,180,824,128.44 = 15 = 7,745,388,275.2292 s2 = s= √7,745,388,275.2292 = 88,007.887573951 Standard error of mean (SEM) sx̄ = s √N = 22,001.971893488 Remainder of the calculations can be found in the appendix for Condamine calculations 8.0 Findings Through further analysis of calculations, it has been concluded that there is some room for error within the data sets. An extra included calculation was standard error of mean. This additional calculation help encompass the interpretive analysis of data interpretation and this calculation fosters that there is some room of error that needs to be considered with calculations. It is to be determined from the calculations that there is all relatively feasible data, this is because all calculations are within a reasonable range of all data points. Also, to be mentioned is that Toogoolawah’s and Condamine’s standard deviation values are highly similar in terms of values. Analysing this point the conclusion that can be made is that both real estate prices don’t vary too much from one another considering any extras or other beneficial components to raise house prices. A distinguishing piece of evidence is provided through calculations such as the Q1 and Q2 calculations having a difference of at minimum 20,000. The biggest difference comes from the first quartile, with this we can identify that Toogoolawah has a higher starting range of house prices overall. Another inclusion is SEM or standard error of mean. This value provides insight to possible error in the calculated mean, the value doesn’t vary too much between prices but the value itself appears to be substantially inordinate. Another result is the inter quartile range between Toogoolawah and Condamine holds a very significant difference allowing for the possibility of a data altering error. 9.0 Reasonableness Data allocated stands within a reasonable and considerable range so that the data can be considered to be feasible for use. All sets of calculations and results with further interpretation such as mean, median and mode calculations even including variance and standard deviation, all values are considered reasonable. It was also determined that grouping data in graphs provides a more viable insight into interpreting data sets and extending on outliers or differences. 10.0 Accuracy and validity An original data set was then altered and made into a bar graph and box and whisker plot to allow for more room for interpretive analysis. This was allowed for to ensure the validity of all data points and calculations proceeding. 11.0 Limitations including only one fixed variable such as just using a 2-bedroom search, using one fixed variable closed the range for more relevant analysis, by doing this it limited the amount of in-depth analysis on particular aspects. It is suspected by doing this included the jump in initial real estate prices for the Toogoolawah data points. By allowing this and keeping it within the final interpretive analysis allowed for a possible margin of error. Conclusion In conclusion the formulated hypothesis deemed to be appropriate in terms of final calculations and analysis of data. The considered hypothesis when checked along with calculations can be interpreted as highly accurate. 12.0 appendix Condamine calculations: Count, N:16 Sum, Σx:6,040,990 Mean, x̄: 377,561.875 Variance, s2: 7,421,876,983.5833 Steps Σ (xi - x̄)2 N-1 (264999 - 377561.875)2 + ... + (569999 - 377561.875)2 = 16 - 1 111,328,154,753.75 = 15 = 7,421,876,983.5833 s = √7,421,876,983.5833 = 86,150.316212904 s2 = (SEM) standard error of mean: sx̄ = s √N =21,537.579053226 Q1 = 304,999 Q3 = 438,000 IQR = 133,001 x˜x~ = 369,999.5 Range = 305,000 Price ($) Condamine frequency 0 - 49,999.99 50,000 - 99,999.99 100,000 - 149,999.99 150,000 - 199,999.99 200,000 - 249,999.99 250,000 - 299,999.99 300,000 - 349,999.99 350,000 - 399,999.99 400,000 - 449,999.99 450,000 - 499,999.99 500,000 - 549,99.99 550,000 - 599,99.99 600,000+ 0 0 0 0 0 4 3 4 2 2 0 1 0 Toogoolawah Frequency 0 0 0 0 0 0 2 8 2 2 1 0 1 Column6 bedrooms Column2 bathroom Column3 car space Condamine price ($) pool extras Column4 car port, animal 1 pen shed, 1 garage car port, shed, 1 garage house 1 264,999 2 1 0 house 2 287,999 2 1 0 house 3 293,999 2 1 0 house 4 299,999 3 1 0 house 5 309,999 2 1 0 house 6 315,000 3 2 0 house 7 333,000 3 2 0 1 garage, large shed garage, shed, 1 animal pens garage, 2 small 2 sheds, garage, car port, 2 shed house 8 365,000 2 2 0 1 garage house 9 374,999 3 2 0 house 10 386,999 3 2 0 2 shed 2 car 2 ports house 11 397,999 3 2 0 1 garage house 12 430,000 2 2 0 1 garage house 13 446,000 2 2 0 house 14 479,999 2 2 0 1 garage shed, 2 garage house 15 485,000 2 2 0 2 garage house 16 569,999 2 2 1 4 garage Toogoolawah price ($) house 1 345,000 2 2 0 2 house 2 347,000 2 2 0 2 house 3 365,000 2 2 0 2 house 4 house 5 366,000 375,000 2 2 2 2 0 0 2 2 house 6 389,000 2 2 0 2 Column3 bedroom/s Column5 bathroom/s Column7 car space pool extras car port car port car port car port garage car port Column11 house 7 house 8 house 9 house 10 house 11 house 12 house 13 394,999 395,000 395,000 397,999 410,000 424,999 454,999 2 2 2 2 2 2 2 2 2 3 2 2 3 2 0 0 0 0 0 0 0 house 14 house 15 house 16 498,999 510,000 700,000 2 2 2 3 3 3 0 0 0 2 2 2 3 3 4 2 garage garage garage garage garage garage car port, shed garage, 2 shed 2 garage 4 garage, 2 sheds