# maths assignment

```CONDAMINE VS
TOOGOOLAWAH
Vince, Jordan
1.0 Introduction ....................................................................................................................................... 2
2.0 Methodology ..................................................................................................................................... 2
3.0 Hypothesis......................................................................................................................................... 3
4.0 Observations &amp; 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 &amp; 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
```