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Houses in California are expensive, especially on the Central Coast where the air is clear, the ocean is blue, and the scenery is stunning. The median home price in San Luis Obispo County reached a new high in July 2004, soaring to \(\$ 452,272\) from \(\$ 387,120\) in March 2004\. (San Luis Obispo Tribune, April 28, 2004). The article included two quotes from people attempting to explain why the median price had increased. Richard Watkins, chairman of the Central Coast Regional Multiple Listing Services was quoted as saying, "There have been some fairly expensive houses selling, which pulls the median up." Robert Kleinhenz, deputy chief economist for the California Association of Realtors explained the volatility of house prices by stating: "Fewer sales means a relatively small number of very high or very low home prices can more easily skew medians." Are either of these statements correct? For each statement that is incorrect, explain why it is incorrect and propose a new wording that would correct any errors in the statement.

Step by step solution

01

Evaluating the first statement

Richard Watkins says that selling fairly expensive houses pulls the median up. This statement can be correct under certain conditions. If the data is organized in ascending or descending order, adding a higher value can shift the median up, especially if the number of data values is even.

02

Evaluating the second statement

Robert Kleinhenz's statement is that fewer sales could increase the influence of very high or very low home prices on the median. This is quite accurate because with fewer data points, any extreme values (either high or low) can significantly affect the position of the median.

03

Conclusional statement

Both statements seem valid under certain circumstances. However, they might lead to misunderstanding if not clarified properly. For the first statement, it might be more accurate to say, 'If expensive houses are sold and if the home prices are evenly distributed, it can potentially pull the median up.' For the second statement, it might be clearer to say, 'With fewer sales, a small number of extreme high or low home prices can cause significant changes to the median.'

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Median

In statistics, the median is a measure of central tendency that represents the middle value of a data set when it is ordered from the smallest to the largest value. The benefit of using the median is that it is less affected by extreme values, or outliers, than the mean. This makes the median a reliable measure for skewed distributions.

To find the median, follow these steps:

• Arrange the data in numerical order from lowest to highest.
• If the number of data points is odd, the median is the middle point.
• If the number of data points is even, the median is the average of the two middle numbers.

For example, in a data set of house prices ranging from \(\\(200,000\) to \(\\)3,000,000\), sorting the data will help accurately compute the median. Hence, if highly expensive homes are added to this sorted list, they might not affect the median directly unless they shift the middle position in the ordered list.

Data Analysis

Data analysis is the process of inspecting, cleaning, and modeling data to discover useful information and inform conclusions. Understanding patterns and trends in data sets allows us to make informed predictions about future outcomes.

In the context of house prices, data analysis involves looking at various aspects, such as price trends, median prices, and sales volume. Analysts may question whether the change in median prices relates to an actual increase in home value or if it's influenced by other factors such as the inclusion of higher-priced properties in the data set. Insights from this analysis can help consumers, real estate agents, and policymakers understand broader market trends.

Outliers

Outliers are data points that differ significantly from other observations. They can drastically affect statistical calculations, including the mean, making the median a less sensitive measure of central tendency when outliers are present.

In real estate, outliers may be properties that are unusually cheap or exceptionally expensive compared to the rest of the market. These properties can skew average prices but have less impact on the median. When analyzing data, it's crucial to identify outliers to understand their effects on the overall data set.

For example, if a few luxury homes are sold at the high end of the market, they can inflate the average price, but the median might remain stable unless these prices begin to shift the middle value of the data. Recognizing the presence of outliers helps ensure that data analysis is not misleading. Proper handling of outliers ensures more reliable and valid conclusions can be drawn from the data.