/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 103 The U.S. Bureau of the Census re... [FREE SOLUTION] | 91Ó°ÊÓ

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The U.S. Bureau of the Census reported a median sales price of new houses sold in March 2014 of \(\$ 290,000\). Would you expect the mean sales price to have been higher or lower? Explain.

Short Answer

Expert verified
The mean sales price is likely higher than the median of $290,000.

Step by step solution

01

Understanding the Terms

The median is the middle value in a data set. The mean is the average of all values in that set. The mean can be influenced more by extremely high or low values compared to the median.
02

Predicting the Relationship

In real estate, the mean sales price is often higher than the median. This is because there can be a few extremely high-value properties that significantly increase the mean, but do not affect the median in the same way.
03

Conclusion Using Patterns

Given that outliers are common in housing prices due to luxury homes, it is reasonable to expect that the mean sales price in this case would be higher than the median sales price of $290,000.

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Key Concepts

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

Median
The concept of median is crucial in understanding data analysis, especially when dealing with real estate statistics. The median is the middle value of a data set when the numbers are arranged in ascending or descending order. If you have an odd number of scores, the median is the exact middle number. If the number of values is even, the median will be the average of the two central numbers.
The median is particularly useful because it is not skewed by extremely high or low values, which are known as outliers. In the context of real estate, where there can be properties that sell for much higher or lower than the average market price, the median provides a clearer picture of the 'typical' price by neutralizing these extremes.
Mean
The mean is more commonly referred to as the average. It is calculated by adding up all the numbers in a data set and then dividing by the count of numbers. This makes the mean sensitive to variations in the dataset, especially to outliers.
In real estate, when you calculate the mean of house prices, extremely high prices (like mansions or beachfront properties) can drag the mean upwards, which might not reflect the price of a typical home. While the mean gives us a sense of the overall market, it's often higher than the median in markets with diverse property values due to the influence of those high-end outliers.
Real Estate Prices
Real estate prices are a fascinating aspect of economics that illustrate broader market trends. They are determined by factors like location, size, amenities, and economic conditions. In most markets, there is a wide range of property values, from small starter homes to luxury estates.
When analyzing real estate prices, both mean and median are used to understand different aspects of the market.
  • The median offers insight into what the typical buyer might expect to pay.
  • The mean can indicate the economic strength and variety in available properties.
Understanding these two measures helps in making informed investment and pricing decisions.
Data Analysis
Data analysis involves collecting, processing, and performing statistical analyses on data to draw meaningful conclusions. For evaluating real estate prices, data analysts use statistical tools to understand market trends and predict future movements.
  • Median and mean are just two of the statistical tools used in data analysis. Other statistical methods like mode, variance, and standard deviation can also be crucial.
  • Data visualization techniques such as graphs and charts are employed to provide a clear view of how values are distributed along the price spectrum.
  • Predictive modeling can be used to forecast future price trends based on historical data.
Effective data analysis helps to identify what statistical methods work best for specific data sets, making it an essential skill for industry professionals in real estate and beyond.

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Most popular questions from this chapter

a. For an exam given to a class, the students' scores ranged from 35 to \(98,\) with a mean of \(74 .\) Which of the following is the most realistic value for the standard deviation: \(-10,1,12,60 ?\) Clearly explain what is unrealistic about the other values. b. The sample mean for a data set equals \(80 .\) Which of the following is an impossible value for the standard deviation? \(200,0,-20 ?\) Why?

Statistics published on www. allcountries.org based on figures supplied by the U.S. Census Bureau show that 24 fatal accidents or less were observed in \(23.1 \%\) of years from 1987 to 1999,25 or less in \(38.5 \%\) of years, 26 or less in \(46.2 \%\) of years, 27 or less in \(61.5 \%\) of years, 28 or less in \(69.2 \%\) of years, 29 or less in \(92.3 \%\) of years from 1987 to \(1999 .\) These are called cumulative percentages. a. What is the median number of fatal accidents observed in a year? Explain why. b. Nearly all the numbers of fatal accidents occurring from 1987 to 1999 fall between 17 and 37 . If the number of fatal accidents can be approximated by a bell-shaped curve, give a rough approximation for the standard deviation of the number of fatal accidents. Explain your reasoning.

True or false: a. The mean, median, and mode can never all be the same. b. The mean is always one of the data points. c. When \(n\) is odd, the median is one of the data points. d. The median is the same as the second quartile and the 50 th percentile.

According to a recent report from the U.S. National Center for Health Statistics, females between 25 and 34 years of age have a bell-shaped distribution for height, with mean of 65 inches and standard deviation of 3.5 inches. a. Give an interval within which about \(95 \%\) of the heights fall. b. What is the height for a female who is 3 standard deviations below the mean? Would this be a rather unusual height? Why?

A company decides to examine the number of points its employees have accumulated in the last two years on their driving record point system. A sample of twelve employees yields the following observations: \(\begin{array}{ccccccccccc}0 & 5 & 3 & 4 & 8 & 0 & 4 & 0 & 2 & 3 & 0\end{array}\) a. The standard deviation is \(2.505 .\) Find and interpret the range. b. The quartiles are \(\mathrm{Q} 1=0,\) median \(=2.5, \mathrm{Q} 3=4 .\) Find the interquartile range. c. Suppose the 2 was incorrectly recorded and is supposed to be 20 . The standard deviation is then 5.625 but the quartiles do not change. Redo parts a and b with the correct data and describe the effect of this outlier. Which measure of variability, the range, IQR, or standard deviation is least affected by the outlier? Why?

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