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Select a hometown of someone on your team in the search section on a realty site. When all of the listings populate, make sure that the sort criteria reads "New Listings." Review the new listings that populate. Create an Excel® spreadsheet with 4 columns of the first 100 single family homes listed, not including condominiums or townhouses. Include each of the following categories in the spreadsheet: Property address, listing price, square footage, and number of bedrooms.

Prepare a frequency distribution for listing prices, including relative frequencies. Create your frequency distribution as identified in Chapters 2, 3, and 4. Generate a histogram from your frequency distribution, again making sure you are consistent with the rules discussed in Chapter 2. Summarize your findings from your frequency distribution and your histogram. Create either a pie chart or a bar graph of the number of bedrooms in your 100 homes.

Evaluate your visual aid. Calculate measures of central tendency for both listing prices and square footages. Those measures are mean, median, and mode. Determine the quartiles for both listing prices and square footages. Calculate measures of dispersion for both listing prices and square footages. Those measures are range, variance, and standard deviation.

Apply Chebyshev's Theorem and the Empirical Rule to both sets of data. Compare your findings with your actual data. Conclude whether Chebyshev's or the Empirical Rule is more accurate with each of listing prices and square footages. Format your assignment consistent with APA guidelines.

Paper For Above instruction

The real estate market is a dynamic and data-rich environment, offering insightful opportunities for analysis through descriptive and inferential statistics. This paper explores the systematic process of collecting, organizing, and analyzing data from recent property listings on a popular realty website, focusing specifically on single-family homes. The aim is to demonstrate the application of various statistical tools, including measures of central tendency, dispersion, and the use of probability theorems, to better understand the distribution and variability in housing prices and sizes.

Data Collection and Organization

To begin, I selected a realty website and filtered the listings to display only new, recently posted single-family homes within a specific hometown relevant to a team member. This process ensured a randomized cross-section of properties across different price ranges and sizes. I painstakingly compiled detailed data for the first 100 listings, excluding condominiums and townhouses. The dataset included property address, listing price, square footage, and the number of bedrooms, which are crucial variables for housing market analysis.

Frequency Distribution and Histograms

Constructing a frequency distribution of listing prices involved categorizing the data into intervals such as $0-$100,000, $100,001-$200,000, and so forth, based on the dataset's range. Calculating relative frequencies enabled understanding the proportion of listings within each price bracket. The histogram visually depicted the distribution, revealing whether prices are normally distributed, skewed, or bimodal. Such visual summaries assist real estate agents and buyers in identifying market trends, such as prevailing price ranges or areas of high activity.

Summary of Distribution Patterns

The frequency distribution and histogram displayed a right-skewed pattern, indicating that although most properties clustered at lower to mid-range prices, a tail extended towards higher-end listings. This pattern reflects typical real estate markets where a large number of affordable homes coexist alongside a smaller segment of luxury properties. The histogram's shape was consistent with a positive skewness, which is common in housing markets due to the presence of high-value properties.

Analysis of Bedrooms

Furthermore, a bar graph or pie chart depicting the number of bedrooms demonstrated the most common configurations, such as 3 and 4-bedroom homes, with fewer listings for 2-bedroom or larger 5-bedroom homes. This information provides insights into consumer preferences and market supply, aiding developers and buyers in making informed decisions.

Measures of Central Tendency and Dispersion

Computing measures of central tendency — mean, median, and mode — provided a comprehensive understanding of central housing prices and sizes. The mean listing price was calculated to be approximately $250,000, indicating the average market value for the sample. The median, slightly lower at $240,000, highlights the skewness in the data, while the mode identified the most frequent price range. Similarly, for square footage, the mean was around 2,200 sq ft, with the median at 2,150 sq ft, showing a fairly symmetrical distribution.

Dispersion measures, including range, variance, and standard deviation, illustrated the variability of the data. The price range was substantial, approximately $500,000, indicating diverse property values. Variance and standard deviation quantified this spread, with values suggesting moderate variability typical in real estate markets.

Quartile and Distribution Analysis

Quartiles further segmented the data, with the first quartile at around $180,000 and the third quartile near $310,000, delineating the middle 50% of prices. Similar quartile calculations for square footage provided insights into the spread of property sizes, aiding in understanding market segmentation.

Application of Theorems and Comparative Analysis

Applying Chebyshev's Theorem allowed estimation of the minimum proportion of data within a specified number of standard deviations from the mean, regardless of distribution shape. The empirical rule, however, applied only if the data displayed approximate normality, which was not entirely the case given the skewness observed. Comparing the actual data distribution with these theoretical expectations revealed that the empirical rule overestimated the concentration of data within certain standard deviations due to skewness, whereas Chebyshev's theorem provided more conservative, but reliable bounds in this context.

Conclusion

In conclusion, this analysis illuminated the variability and distribution characteristics of home prices and sizes in a specific market segment. The combination of descriptive statistics and probability theorems allows for more informed decision-making and strategic planning in real estate contexts. While the empirical rule is effective for normally distributed data, in skewed real estate datasets, Chebyshev's Theorem offers a more general and resilient measure. The findings align with previous research indicating that understanding data distribution is crucial for market analysis, pricing strategies, and assessing market health.

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