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Graph-Number of New home Sales

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Graph-Number of New home Sales [#permalink] New post 11 Feb 2013, 12:23
A real estate agent did research to compile the number of new home sales in five different cities, for each of the years 2004, 2006, 2008, and 2010. Each number indicates the total number of new homes sold in that city in that year, regardless of when construction started on each home.

From the drop-down menu, select the option that creates the most accurate statement based on the information provided.

Q) The city with the greatest variance in new home sales during the 4 years is
Antioch
Lindenhurst
Round Lake
Spring Grove
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Re: Graph-Number of New home Sales [#permalink] New post 12 Feb 2013, 20:44
Expert's post
fameatop wrote:
A real estate agent did research to compile the number of new home sales in five different cities, for each of the years 2004, 2006, 2008, and 2010. Each number indicates the total number of new homes sold in that city in that year, regardless of when construction started on each home.

From the drop-down menu, select the option that creates the most accurate statement based on the information provided.

Q) The city with the greatest variance in new home sales during the 4 years is
Antioch
Lindenhurst
Round Lake
Spring Grove


If the values are around the mean, the variance is low. If the values are far away from the mean, the variance is high. (Variance is just the square of SD and hence is based on the same concepts)
The dark blue line (Antioch) shows maximum variation since in 2004, home sales was 50 and in 2008, it was 350. On the number line, the sales of Antioch would be further apart from the mean than those of any other city.
Answer: Antioch

On the same lines, the variation will be least in the case of Spring Grove.
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Re: Graph-Number of New home Sales [#permalink] New post 12 Feb 2013, 23:14
Expert's post
fameatop wrote:
A real estate agent did research to compile the number of new home sales in five different cities, for each of the years 2004, 2006, 2008, and 2010. Each number indicates the total number of new homes sold in that city in that year, regardless of when construction started on each home.

From the drop-down menu, select the option that creates the most accurate statement based on the information provided.

Q) The city with the greatest variance in new home sales during the 4 years is
Antioch
Lindenhurst
Round Lake
Spring Grove

Received PM.

Hi Fame,

Variance is a measure of how far data points of a dataset are spread w.r.t. mean.

We are interested in fetching a single value as variance that will be a representative value for all deviations of the data points. As a thumb rule, more the spread (range) of data points from mean value, more the variance could be and vice versa. there are exception to this.

Here, you should apply your best estimation - which variance value would be greater than the other? It is quite obvious that project Antioch will have the highest value of variance among all projects, because it has the highest range (350-50=300) among all projects. The three extreme data points (350, 50 and 50) will increase the values of deviations to higher level. So the answer is Antioch.

Hope this helps. :-)

Shalabh
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Re: Graph-Number of New home Sales   [#permalink] 12 Feb 2013, 23:14
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