Greater Northwest Indiana Realtors Association (http://www.gniar.com/)has a lot
ID: 3041729 • Letter: G
Question
Greater Northwest Indiana Realtors Association (http://www.gniar.com/)has a lot of data on real estate prices for Northwest Indiana. The real estate prices for 100 single family homes (list prices) are between $30000 and $800,000 with average home price as $200,000. Some new homes from Crown Point costing over a million dollars were listed recently.
If you were doing a story for the Times about the housing market in Northwest Indiana, which measure of central tendency and dispersion would you use to describe the average price and why? Would it make a difference if you use mean or median time as a measure of central tendency? Discuss the pros and cons of each measure in this case.
Explanation / Answer
In this case it would be better to use median as the appropriate measure of central tendency and mean deviation about median aas ththe appropriate measure of dispersion to describe the average price.
This is because mean as a measure of central tendency is highly affected by the presence of extreme values. The new homes listed recently, after calculation of the average, all cost over a million dollars, which is very high as compared to the present average price. Thus, these new prices can be considered as extreme or outlying values. Mean being highly sensitive to extreme values, will be greatly affected by the addition of these new prices, thus increasing the average too much, leading the readers to believe that the prices are very high in general, which is not the case.
On the other hand, median is a measure of central tendency that takes into account the number of observations and considers the observation in the middle-most position in ascending or descending order as the average. As a result, adding those high priced houses in the list would, at most, shift the middle-most position a few places, thus taking a slightly higher observation as the average. But this value would not be too high as median does not take into account the magnitude of the observations. Thus considering median is better than considering mean in this situation.
Similarly, mean deviation about median, being based on the median, is much more stable and gives a far better picture of the dispersion in this case, than mean based measures like mean deviation about mean or standard deviation, because these measures being based on mean - an unreliable measure of central tendency in this situation - gives unreliable measures of dispersion.
Hence it is better to use median as the measure of central tendency and mean deviation about median as the measure of dispersion here.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.