bussines statistic

Question

Real Estates Sales ?The Association of Real Estate Agents for Foreign Properties (AREAFP) is a local body representing agents who promote sales of foreign properties in Singapore. The objectives of AREAFP are to promote and protect the interests of estate agents as well as to protect the interests of members of the public who engage the services of estate agents for the purchase of foreign properties. With the sharp decline in property prices in US, AREAFP noted its members’ feedbacks that there was an increase in interest on US properties. With this in mind, Mr Peter Tan, the Executive Director of AREAFP would like to publish an article on the association monthly magazine regarding sales prices of US properties. In particular, he wishes to identify the price distribution of different cities. Incidentally, Mr Tan has a good friend who is a real estate agent in US. From this friend, Mr Tan managed to obtain some recent sales record of properties for two cities. Mr Tan has engaged your service to conduct a relevant statistical analysis and offer some insight into descriptive statistics of the property prices in these two cities. 
Question 1 As a preliminary exploration of the data, generate some diagrams and determine the appropriate descriptive statistics for both cities. Write a short comment for EACH of the diagram.

 Question 2 Based on the statistical analysis done in Question 1, discuss your observations and highlight three possible statistical concerns. Keep your answer within 300 to 400 words (indicate your word ?count). 

Answer 1

Hi Mellanie,

Happy to walk you through how to approach this. One thing up front: the answer depends on the actual price data for the two cities, so plug your numbers into the spots I've bracketed and you'll be set. Here's how I'd structure both questions.

QUESTION 1. Diagrams and descriptive statistics

Since property prices are quantitative data, these are the diagrams that fit:

1. Histogram (one for each city). This shows the shape of the price distribution, meaning where prices bunch up and whether there's a long tail.
2. Comment to adapt: "The City A histogram is unimodal and skewed to the right. Most homes sit in the lower and middle price bands, with a thin tail of expensive properties stretching to the right. That pattern is normal for housing, where a handful of high-end sales sit well above the rest of the market."
3. Box-and-whisker plot, both cities on the same axis. This is the most useful chart here because it lets you compare the two cities directly on median, spread, and outliers.
4. Comment to adapt: "City B's box sits higher and is taller than City A's, so City B has both a higher median price and more price variation. The points past City A's upper whisker are outliers, probably premium homes, and they are what pull City A's mean above its median."
5. Stem-and-leaf display. This shows the shape while keeping the actual values, which works well for a small dataset.
6. Comment to adapt: "The stem-and-leaf backs up the right skew from the histogram and lets you read the individual prices, so you can see the cluster in the mid-range and the isolated high values clearly."

For the descriptive statistics, build a side-by-side table for the two cities and include:

1. Central tendency: mean, median, mode
2. Dispersion: range, interquartile range (Q1 and Q3), variance, standard deviation, and the coefficient of variation
3. Shape: skewness and kurtosis
4. Five-number summary: minimum, Q1, median, Q3, maximum

The key point to make: if the mean is greater than the median, the prices are skewed right, and the median is the better measure of the "typical" price. Say that directly in your comments.

QUESTION 2. Observations and three statistical concerns (337 words)

The analysis shows that property prices in both cities are skewed to the right rather than symmetric. In each city the mean is higher than the median, which tells us a small number of expensive sales are pulling the average up. Because of that, the median [City A: $; City B: $] is a more reliable measure of the typical property than the mean. City B has both a higher median and a larger standard deviation, so it is not only pricier on average but also more spread out, and buyers there face a wider range of prices. The box plots show the same thing, with City B sitting higher and wider, while City A carries a few outliers on the high side.

Three concerns hold the conclusions back.

The first is that the sample is not random. The data came from one contact's recent transactions, not a random draw from either city's market. That creates selection bias, because those properties may reflect a single agent's price segment rather than the city overall. The results cannot be safely generalized to either city, let alone to the wider U.S. market the article is meant to describe.

The second is that the skew and the outliers weaken the mean and the standard deviation. Both measures react strongly to extreme values, so any comment built on the mean risks overstating the typical price. The median and the interquartile range are steadier here and should lead the discussion.

The third is that the two cities are not compared on equal footing. The sample sizes are likely different, and nothing controls for property type, size, bedrooms, age, or location. A straight price comparison may just be picking up a different mix of properties rather than a real difference in market value. Use the coefficient of variation instead of the raw standard deviation to compare the variability fairly.

The data gives useful early insight, but the sampling method and the lack of comparability make it too thin to support firm claims in a published article.

Hope this helps. Happy to check your charts once you've run them.