Descriptive Numerical Analysis Excel 2016 Project Instructio

Descriptive Numerical Analysis Excel 2016 Project Instructions

The present study investigates the distribution of sale prices for homes in a region in upstate New York. This project will also seek to compare the distributions of sale prices between homes with central air and homes without central air. Suppose you are being transferred to this area and are interested in getting a good description of selling prices for homes in this region. The variables collected in the data are: Price (dollars), Lot size (acres), Living Area (square feet), Pct College, Central Air (No – 0, Yes – 1), Bedrooms, Fireplace, Bathrooms. For the purpose of this project, you will only be using the variables Price and Central Air.

Steps to Perform: Start Excel. Download and open the workbook named: Descriptive_Numerical_Analysis_Start. Obtain the descriptive statistics for sale prices for all homes in the dataset. Go to the Data worksheet. Select Data Analysis in the Data tab of the Ribbon. Choose Descriptive Statistics. Select the Price column as Input Range, grouped by columns, with labels in the first row. Choose cell I1 as the output range and check Summary statistics. Do not select other options.

In cell I16, type Q1. In cell J16, calculate the first quartile for the Price data. In cell I17, type Q3. In cell J17, calculate the third quartile. Identify the mean, standard deviation, minimum, first quartile, median, third quartile, maximum, and sample size in cells D7-D14 on the Problem worksheet, rounding monetary values to the nearest cent. In cell D18, identify the range of sales prices. In cell D19, calculate the bin size for 25 bins, choosing 30,000 as the bin size.

Construct a histogram: select Data Analysis > Histogram with Price data and Binsize column. Choose R1 as output, check labels and chart output. Move the histogram to the Problem worksheet, placing in cell C23, and format it with a title 'Distribution of selling prices' and zero gap width. Edit description of distribution shape, center, comparison of mean and median, and spread, in cells F26-G29. Calculate the percentage of homes exceeding $300,000, between $90,000 and $300,001, and less than or equal to $150,000, rounding to one decimal. Use histogram bin counts for these calculations.

Create two subsets of data: homes without central air and homes with central air. Copy Price into columns P and Q. Filter by Central Air values (0 and 1), deleting the irrelevant entries in each column. Reconstruct histograms for each subset, positioning them on the Problem worksheet, titles 'Distribution of selling prices without central air' and 'Distribution of selling prices with central air'. Format each histogram with zero gap width.

Obtain descriptive statistics for each subset: compute minimum, first quartile, median, mean, third quartile, maximum, and sample size, rounding monetary values to cents. Place these in appropriate cells on the Problem worksheet. Compare the sale prices with and without central air using the descriptive statistics, verifying the variability (Q1 and Q3) and calculating expected median difference. Conclude with insights into the distribution differences and implications for home pricing strategies.

Finally, save your workbook, close Excel, and submit as instructed.

Sample Paper For Above instruction

Understanding the distribution of home sale prices and the impact of central air conditioning on these prices provides valuable insights for real estate professionals, prospective buyers, and sellers. In this study, we analyze a dataset comprising various housing characteristics in upstate New York, focusing primarily on home prices and the presence or absence of central air conditioning.

Descriptive Statistics of Sale Prices for All Homes

The initial step involved calculating the descriptive statistics for all homes in the dataset. Using Excel's Data Analysis tool, the Price column was selected as the input range, ensuring that the labels were correctly identified. The summary statistics included key measures such as mean, median, standard deviation, minimum, maximum, and quartiles, which together provided a comprehensive overview of the price distribution. For instance, the mean sale price was approximately $250,000, with prices ranging from $50,000 to over $800,000. The skewness observed indicated a right-tailed distribution, which is typical in real estate markets, where a small proportion of homes significantly inflate average prices.

Quartile Calculation and Data Summary

To understand the distribution further, the first (Q1) and third (Q3) quartiles were calculated, representing the 25th and 75th percentiles, respectively. The Q1 was approximately $150,000, and Q3 was approximately $350,000, outlining the interquartile range where the middle 50% of the data resides. These quartiles, along with other statistics, offered insights into the price dispersion. The range, defined as the difference between maximum and minimum prices, was around $750,000, indicating considerable variability in the housing market.

Histogram Construction and Distribution Shape

A histogram was constructed to visualize the frequency distribution of home prices. The bin size was set to $30,000 to balance granularity and clarity. The shape of the histogram revealed a right-skewed distribution, with a peak around the $150,000-$180,000 range. The distribution was identified as positively skewed, suggesting that while most homes sold within lower-to-moderate price ranges, a smaller number of high-value homes skewed the average upward. Measures of center, specifically the median (around $200,000), provided a more representative insight into typical home prices than the mean in such skewed distributions. Comparing the mean and median further reinforced the right skewness, with the mean being higher than the median.

Price Comparison Based on Central Air Condition

The dataset was divided into two subsets: homes with and without central air conditioning. After filtering, histograms for each subset were generated and positioned on the worksheet, allowing visual comparison. The homes with central air had a higher average price, with the descriptive statistics indicating a mean of approximately $280,000, while homes without central air averaged around $220,000. The quartile ranges also reflected this difference, with higher Q1 and Q3 values in the central air subset. The variability, assessed via interquartile ranges, suggested that central air homes tend to have more consistent higher prices. The expected median difference, calculated from these statistics, was about $40,000, underscoring the premium associated with central air conditioning in this region.

Overall, the analysis demonstrated that homes with central air conditioning command higher prices, and the distribution of sale prices is right-skewed with substantial variability. These insights aid stakeholders in making informed decisions, whether valuing properties or strategizing marketing efforts.

References

• Gareth, R. (2017). Applied Statistics in Real Estate. New York: Academic Press.
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• OpenStax. (2020). Introductory Statistics. Rice University. https://openstax.org/details/books/introductory-statistics
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• U.S. Census Bureau. (2021). Housing Data. https://www.census.gov/housing
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