Gulf View Inc, Sales
Introduction
Location (Gulf view or no Gulf view) of a condominium and property listing prices are very essential part of number of days it takes to sell a property and real estate sales price. An understanding of how location of a condominium, the sales price, listing price, and the duration of time in days it takes to sell are very important to real estate firm like Gulf Real Estate Inc. Analysis of the data provided on sales of 18 NonGulf view condominiums and 40 Gulf view condominiums can provide understanding into extra development of upcoming sales. Gulf Real Estate sampled data from several listed services in Naples, Florida (Gibson & Li, 2013), (Matthews, 2014).
The sample recorded the location of the condominium, listing price, selling price and the duration it takes to close the sale (days) for each unit. The aim of carrying out the analysis is to determine if the location of a condominium or listing price influences selling price or the duration it takes to close the sale (days). The industry of real estate is a booming industry in Florida and the US as whole since the prices of condominiums are ever increasing every day (Mathews, 2014). There is predicted prosperity in this industry. Therefore, analysis of data from the industry is of great concern to stake holders in the industry. This paper will involve analysis and interpretation of data provided by Gulf View Inc.
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Overview of Condominium Sales in Florida
Gulf View Condominium
Considering the 40 Gulf view condominium sales totaling $23,034,000 was registered, giving an average of $575,850 per condominium. The listing price for condominium having gulf view ranged from $185,000 to $995,000 with a range of $810,000 (Singpurwalla, 2013). However, the real selling price ranges from $181,100 to $959,400, with the duration it takes to close the sale (days) ranging from 17 to 295 days with a range of 278 days. The standard deviations are $246,942, $237,010 and 77 for listing price, selling price, and the duration it takes to close the sale (days) respectively. The summary of the set of the data is represented in table 1 below.
Table 1
Condominium with Gulf View Condominium

Listed Price ($) 
Selling Price ($) 
Duration (Days) 
Mean 
603,475 
575,850 
157 
Median 
605,500 
581,600 
172 
Std. Dev 
246,942 
237,010 
77 
Min Value 
185,000 
181,100 
17 
Max Value 
995,000 
959,400 
295 
Range 
810,000 
778,300 
278 
Sum 
24,139,000 
23,034,000 





Source: Authors (2017)
Outliers  There existed outliers in every category (Listed price, selling price, and duration to sell). For analysis purpose a value is considered an outlier if it is greater than third quartile minus the product of 0.5 and third quartile (upper bound), or if it is less than first quartile minus the product of 0.5 and interquartile range (lower bound). In mathematical expression, Q1 – first quartile, Q3 third quartile and IQR Interquartile range (Q3Q1). An Outlier(OT) is given as; (Q1 – 0.5*IQR) < OT > (Q3 + 0.5*IQR) as used in the excel sheet (Singpurwalla, 2013). In most calculations 1.5 times interquartile range is used to determine outliers in a data set, but for this analysis 1.5 gave negative values, therefore, the researchers decided to use 0.5 times the interquartile range meaning that the results may be biased. The outliers are listed in the table 2 below.
Table 2
Outliers for Gulf View Condominium
Listed Price 
Selling Price 
Duration (days) 

Greater 
Less 
Greater 
Less 
Greater 
Less 
975,000 
196,000 
959,400 
181,000 
295 
41 
965,000 
185,000 
945,700 
184,000 
292 
35 
960,000 
942,300 
33 

995,000 
944,000 
19 

48 
Source: Authors (2017)
Greater has been used to show values that are exceeding the upper bound while less has been used to show values that are less than the lower bound.
No Gulf View
The 18 No Gulf view condominium gave a total of $3,825,100 giving an average of $212,506 per condominium with an average number of days to sell of 180 days. The listing price for condominium with No Gulf view ranged from $135,000 to $281,000 with range of $146,000 and the number of days to sell ranged from 34 to 346 days (Singpurwalla, 2013). However, the sale price ranged from $131,400 to $277,300. The standard deviations are $45,233, $44,340 and 102 days for listing price, actual selling price and the duration it takes to close the sale (days) respectively. The summary of the set of data is shown in table 3 below.
Table 3
Condominium with No Gulf View
Listed Price ($) 
Selling Price ($) 
Duration (days) 

Mean 
220,7778 
212,506 
180 
Median 
232,000 
226,350 
186 
Std. Dev 
45,233 
44,340 
102 
Min Value 
135,000 
131,400 
34 
Max Value 
281,000 
277,300 
346 
Range 
146,000 
145,900 
312 
Sum 
3,974,000 
3,825,100 

Source: Authors (2017)
Outliers  Listed price, selling price and duration to sell all have outliers. A value is considered an outlier if it is less than first quartile minus the product of 0.5 and interquartile range (lower bound) or if it is greater than third quartile minus the product of 0.5 and third quartile (upper bound). The outliers are summarized in the table 2 below.
Table 4
Outliers for No Gulf View Condominium
Listed Price ($) 
Selling Price ($) 
Duration (Days) 
135,000 
131,400 
341 and 346 
Source: Authors (2017)
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Interpretation of Results
The average selling price for condominium with gulf view ($575,850) is greater than average selling price for condominium with no gulf view ($212,506). This is a very important statistic for a real estate agent in understanding the condominium market. This shows that condominiums with gulf view sell at very high prices compared to those without gulf view. According to AngjellariDajci et al. (2015), one of the most important considerations when buying a house is location. Therefore, real estate agent can be able to know how to price condominium based on the location of the property. Another interesting result is that of average days taken to sell a condominium. For gulf view, the average duration it taken to close sale (days) is 157 while for no gulf view is 180 days, meaning that condominiums with gulf view sell faster than those without. This information is very important for a real estate agent since they can change sales strategies if the duration taken to sell a condominium exceeds the average or falls below the average. For instance, they can carry out more advertising or reduce the advertisement cost.
The data shows that on average, Gulf view condominium sell for $575,850, which is higher than the average selling price of no gulf view condominium that goes for an average of $212,506. However, their selling price have a higher standard deviation ($237,010) than that of condominium without gulf view ($44,340) this indicates that the selling price of Gulf view condominium fluctuates more than that of condominium without gulf view. This implies that condominium with no gulf view might have low selling price, but their prices are consistent for each sale. This information can help real estate agent to plan sales for condominium.
In both cases the mean and the median are very close, meaning that the outliers had little effect on the measures of central tendency. This implies that the data is approximately normally distributed. The information can assure real estate agent that the business is on truck and that there are no highly potential aspects of the condominium that requires attention.
The range of the data shows how the data is distributed with respect to maximum and minimum values. This is very essential to real estate agents as they can use this information to approximate their worse sales and hence prepare for the worst, or they can predict prosperity for the industry. In statistical analysis, maximum and minimum values are not only used in determination of range, but they can be used to analyze the distribution of the sample chosen, hence giving a clue on whether the sample size was sufficient on its own or the size should be increased.
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Confidence Interval
Gulf View
The confidence intervals for gulf view condominiums are calculated using standard normal distribution since the sample size of 40 is greater than 30, meaning, normal distribution can be used. 95% significance level is used. Mathematically the confidence interval is represented as; Estimated Mean ( ) ± Margin of Error (ME).
Where, ME = , SD – Standard deviation, Z= 1.96 for α =0.05 and n sample size (Singpurwalla, 2013). Using the above formula confidence interval for selling price and duration taken to sell are constructed
Selling price the confidence interval is 575,850 ± 73,449. This interval shows that the population average selling price lies between $502,401 to $649,299. That is 95% of the time the population average selling price of a gulf view condominium will fall within the boundaries of the confidence interval constructed. The data can therefore be used to estimate minimum and maximum total sales expected from available gulf view condominium in Florida. This information is very vital in negotiation of selling price to customers (Gibson & Li, 2013).
Duration to sale – Using the same approach as in the case of selling price, the confidence interval for the duration taken to close the sale (days) of a condominium with gulf vies is 158 ± 24, meaning that the population average duration of time to sell a condominium lies between 134 to 182 days. The interpretation of the result is that if we were to repeat the experiment several times and calculate the confidence interval every trial, the resulting confidence intervals we will obtain must include the population average 95% of the time. That is, there is 95% probability that any specific confidence interval will contain the population average. The information can be used to estimate prices that will have the effect of reducing the duration it takes to close the sale (days) for a gulf view condominium, taking into account profit margins and any potential loss (Singpurwalla, 2013).
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No gulf View
The confidence intervals for no gulf view condominiums are calculated using student’s t test because the sample size of 18 is less than 30, meaning, normal distribution cannot be used (small sample size). Mathematically the confidence interval is represented as; Estimated Mean ( ) ± Margin of Error (ME).
Where, ME = , SD – Standard deviation, t = 2.1090 for α =0.05 degrees of freedom 17 (18 1) and n sample size. Using the above formula confidence interval for das taken in order to sell is constructed.
Selling price the confidence interval is 212,506 ± 22,048. This interval shows that the population average selling price lies between $190,458 to $234,554, meaning, if several samples were to be collected then 95% of the time the population average selling price for no gulf view condominium would be within the constructed confidence interval (Bin & Kruse, 2006).
Duration to sale – employing a similar method, the confidence interval is 180 ± 59, meaning that the population average duration of time to sell a condominium lies between 121 to 239 days. A real estate agent would use this information in projection of sale hence improve planning in real estate business (Bin & Kruse, 2006).
Estimations Based on Set Targets
In this section, manual calculations are used to determine sample size since it involves reverse process in excel. Starting with case where the branch manager requests for margin of error to be $40,000 for gulf view condominium, then the sample size is determined as:
Margin of error (ME) = where SD sample standard deviation, Z is the 95% significance level standard Z score is 1.96, and n is the sample size (Singpurwalla, 2013).
Implying, n = = = 135 condominiums.
Second is the case where the branch manager requests for margin of error to be $15,000 for condominium with no gulf view, then the size of the sample is determined as:
Margin of error (ME) = where SD sample standard deviation, t tabulated student’s t value at 95% significance level, the t value 2.1090, and n is the sample size.
Implying, n = = = 39 condominiums.
Forecasted Selling Price and Time taken to Sell
In this section scatter diagrams with trendline is used to estimate the selling price and time taken to sell.
Gulf View Condominium
For gulf view figure 1 below show scatter diagram between listed price and the selling price for gulf view condominium.
Using the line of regression where y represents sale price and x represent list price we can determine sale price. Given list price of $589,000, sale price, y = 0.958(589000) – 2,265 giving sale price of $561,997.
In the case of days required to sell the gulf view scatter plot for days to sale against, list price as shown in figure 2 below.
Using the line of regression where y represents days to sale and x represent list price we can determine days taken to sell the condominium given list price of $589,000 as y = 0.0294(589000) + 17517 giving number of days as 200 days.
No gulf View Condominium
For no gulf view figure 3 below shows scatter diagram between listed price and the selling price for no gulf view condominium.
Using the line of regression where y represents sale price and x represent list price we can determine sale price. Given list price of $285,000, sale price, y = 0.958(285000) – 2,526 giving sale price of $275,064 (Singpurwalla, 2013).
In the case of days required to sell the no gulf view condominium, a scatter plot for days to sale against list price as shown in figure 4 below.
Using the line of regression where y represents days to sale and x represent list price we can determine days taken to sell the condominium given list price of $285,000 as y = 0.0838(285000)  23533 giving number of days as 350 days.
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References
 AngjellariDajci, F., Cebula, R. J., & Boylan, R. (2015). Firm size, dual brokerage, and National Franchise Affiliation of Real Estate Brokerage Firms: Unexpected results for the period 2008–2013. Journal of Housing Research, 24(2), 175191.
 Bin, O., & Kruse, J. B. (2006). Real estate market response to coastal flood hazards. Natural Hazards Review, 7(4), 137144.
 Gibson, H. J., & Li, Y. (2013). Opportunities for the United States condominium foreclosure market to provide amenable affordable housing options: The case of Tampa/Hillsborough, Florida. Urbani izziv, 24(1), 90106.
 Matthews, W. C. (2014). Aventura Management, LLC v. Spiaggia Ocean Condominium Association: Condominium Associations Beware. Fla. L. Rev., 66, 1731.
 Singpurwalla, D. (2013). A Handbook of Statistics: An Overview of Statistical Methods (1st ed.). Bookboon: Bookboon.
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