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Chapter 1: Problem 10

You look at real estate ads for houses in Naples, Florida. There are many houses ranging from \(\$ 200,000\) to \(\$ 500,000\) in price. The few houses on the water, however, have prices up to \(\$ 15\) million. The distribution of house prices will be a. skewed to the left. b. roughly symmetric. c. skewed to the right.

Short Answer

Expert verified
The distribution is skewed to the right.

Step by step solution

01

Understanding Skewness

Skewness in a distribution refers to whether the tail of the distribution is longer on one side than the other. In this case, if high-priced houses on the water extend the distribution to the right, the distribution is considered skewed to the right.
02

Analyzing the Price Range

Most houses are priced between \(\\( 200,000\) and \(\\) 500,000\), which represents the bulk of the data. However, exceptional cases priced at up to \(\$ 15\) million exist, which are much higher than the typical range.
03

Identifying the Skew Direction

Since the few very expensive houses create a long tail on the higher end of the price scale, the tail extends to the right. This means the distribution has a right skew.

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Key Concepts

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

Distribution Symmetry
In statistics, the concept of distribution symmetry revolves around the way data is spread across its range. A dataset is considered symmetric if the left and right sides of the histogram are approximate mirror images of each other. This implies that the data has balanced distribution on either side of the central point.

Understanding distribution symmetry is crucial for interpreting data patterns. When analyzing data, checking for symmetry helps determine if using certain statistical measures like the mean or median is appropriate.
  • If a distribution is perfectly symmetric, the mean and median will be the same.
  • Skewness challenges symmetry, resulting in either right or left skew.
  • Understanding whether data deviate from symmetry can help make inferences about the population being analyzed.
Right Skew
Right skewness, or positively skewed distribution, happens when the right tail (high-value end) of the distribution is longer or fatter than the left tail. This type of skewness means that there are outliers or values in the dataset that are higher than the majority of the data points.

When a distribution demonstrates a right skew:
  • The mean will typically be greater than the median since the exceptional high values pull it upwards.
  • This skewness can affect the interpretability of data, as the typical value (median) may be much lower than the mean due to the long tail.
  • It's important to consider this type of skewness when applying statistical models because it might require data transformation to achieve normality.
Real Estate Price Distribution
The real estate market is a classic example where understanding distribution is vital. Specifically, when looking at the distribution of house prices in a place like Naples, Florida, we encounter varied price points depending on factors like location and amenities.

In such scenarios:
  • The bulk of the houses are priced within a common range, often matching most buyers' budget.
  • Fewer houses are priced extremely high, especially if they have premium features such as waterfront access.
  • This results in a distribution that skews to the right, due to the high-priced outliers.
Understanding this skew is crucial for buyers, sellers, and analysts because it affects real estate market predictions and evaluations.

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Most popular questions from this chapter

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