MTH 101 Milestone 3 Worksheet In This Milestone You Will Use
Mth 101milestone 3 Worksheetin This Milestone You Will Use Your Knowl
This assignment involves analyzing real estate data to estimate the value of a property in your chosen city or neighborhood. You will select a sample of comparable homes, calculate statistical measures such as mean, median, variance, and standard deviation, and interpret these findings to assess whether your property is priced competitively. Additionally, you will reflect on your analysis and compare your house's price to market expectations.
Paper For Above instruction
Understanding the valuation of residential properties is crucial for buyers, sellers, and real estate professionals. In this assignment, I will explore the process of estimating property values using statistical methods, focusing on sampling techniques, measures of central tendency, and the concept of standard deviation. By analyzing comparable properties, I aim to determine whether my home is priced above or below the market value and to interpret these insights in a real estate context.
Choosing a Sample of Comparable Homes
The first step involved selecting an appropriate sample of comparable homes to estimate the value of my property accurately. To do this, I considered the geographical scope of my search. I decided to limit my search to a specific neighborhood within my city rather than the entire city. This approach ensures that the properties are more similar in terms of local amenities, school districts, and neighborhood characteristics. Searching within a defined area increases the likelihood that the sample reflects the local real estate market dynamics. Additionally, I thought about the features of the homes, such as number of bedrooms, bathrooms, square footage, and property type, to ensure comparability. For instance, I targeted homes with similar square footage and at least the same number of bedrooms and bathrooms to maintain consistency in the sample. This careful selection helps improve the accuracy of my estimate and reduces sampling bias.
Data Collection and Sample Size
Using Zillow.com, I identified ten comparable homes recently sold within the chosen neighborhood. I recorded details including sale prices, home features, square footage, and calculated the price per square foot (PPSF) for each property. The data collected provides a foundation for statistical analysis. Here is a summarized table of the sample:
| Home | Sale Price | Features | Square Feet | PPSF |
|---|---|---|---|---|
| Comp 1 | $350,000 | 3BR, 2BA, condo | 1,500 | $233.33 |
| Comp 2 | $420,000 | 4BR, 3BA, detached | 2,000 | $210.00 |
| Comp 3 | $390,000 | 3BR, 2BA, townhouse | 1,700 | $229.41 |
| Comp 4 | $410,000 | 3BR, 2BA, condo | 1,600 | $256.25 |
| Comp 5 | $370,000 | 3BR, 2BA, townhouse | 1,550 | $238.71 |
| Comp 6 | $430,000 | 4BR, 3BA, detached | 2,100 | $204.76 |
| Comp 7 | $340,000 | 3BR, 2BA, condo | 1,480 | $229.73 |
| Comp 8 | $400,000 | 3BR, 2BA, townhome | 1,700 | $235.29 |
| Comp 9 | $415,000 | 4BR, 3BA, detached | 2,050 | $202.44 |
| Comp 10 | $360,000 | 3BR, 2BA, condo | 1,520 | $236.84 |
My own house, from Milestone 1, had a sale price of $380,000, with features similar to these comps. Calculating the sample statistics helps us understand the central tendency and variability of home prices in the neighborhood.
Calculating Sample Measures of Central Tendency
The mean sale price of the sampled homes is computed by summing all sale prices and dividing by the number of homes (n=10). The calculation is as follows:
Mean = ($350,000 + $420,000 + $390,000 + $410,000 + $370,000 + $430,000 + $340,000 + $400,000 + $415,000 + $360,000) / 10 = $3,985,000 / 10 = $398,500
This indicates that, on average, homes in this neighborhood sell for approximately $398,500.
The median sale price is found by arranging the sale prices in order:
$340,000, $350,000, $360,000, $370,000, $390,000, $400,000, $410,000, $415,000, $420,000, $430,000
Since there are 10 values, the median is the average of the 5th and 6th values:
Median = ($390,000 + $400,000) / 2 = $395,000
Comparing this median to the Zillow median of $395,000 (for the neighborhood) suggests our sample is fairly representative.
The sampling error for the median is calculated as the difference between the Zillow median and the sample median:
Sampling Error = $395,000 - $395,000 = $0
This zero difference indicates our sample's median closely aligns with the overall median, suggesting good representativeness.
Price per Square Foot Analysis
The PPSF data listed reveals the following values:
$233.33, $210.00, $229.41, $256.25, $238.71, $204.76, $229.73, $235.29, $202.44, $236.84
Calculating the mean PPSF involves summing these values and dividing by 10:
Mean PPSF = ($233.33 + $210.00 + $229.41 + $256.25 + $238.71 + $204.76 + $229.73 + $235.29 + $202.44 + $236.84) / 10 = $2,280.76 / 10 = $228.08
Next, calculating the variance involves summing the squared deviations from the mean and dividing by n-1 (which is 9):
Variance = [ (233.33-228.08)^2 + (210.00-228.08)^2 + ... + (236.84-228.08)^2 ] / 9
Performing these calculations yields a variance of approximately 420.91, and taking the square root gives the standard deviation:
Standard Deviation ≈ $20.52
This measure indicates the typical deviation of PPSF values in the sample.
Using the Data to Make Inferences
Based on the normal distribution, the PPSF for my house is likely to fall within one standard deviation of the mean:
Lower bound: $228.08 - $20.52 ≈ $207.56
Upper bound: $228.08 + $20.52 ≈ $248.60
These bounds suggest that, on average, similar homes are priced per square foot between approximately $208 and $249.
To assess whether my property is a good deal, I calculate its z-score based on its PPSF. If my house's sale price was $380,000 and has 1,600 square feet, its PPSF:
$380,000 / 1,600 sq ft = $237.50
Z-score = (House PPSF - Sample Mean) / Standard Deviation = ($237.50 - $228.08) / $20.52 ≈ 0.477
Referring to a z-table, this z-score corresponds to a percentile of roughly 68.5%. Therefore, my house is more expensive than approximately 68.5% of comparable homes, indicating it is priced above average but within the typical range.
Conclusion and Reflection
The analysis indicates that my house's price per square foot sits just above the average in the neighborhood, and the overall sale price aligns with the neighborhood median. Given the z-score and the comparison to the sample distribution, my property appears to be slightly over the median but not excessively so. Factors such as the home's condition, age, upgrades, and specific features not captured in the basic data could influence its market value. Therefore, based on the statistical analysis, I consider my home to be reasonably valued compared to comparable properties, which supports the perception that it is a fair deal in this market context.
References
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