Thread: Averages - explaining answers

Hello, I found this forum through a nearly abandoned Usenet group. Here are prices for 10 homes. The problem at hand asked me to find the mean, median and mode of these housing prices.

$120,000 $122,000 $125,000 $125,000 $139,000
$145,000 $167,000 $210,000 $540,000 $950,000

Answer: The mean average is $264,300. The median is $142,000. The mode is $125,000.

The problem then asked "Which measure of "average" best describes the average housing price for the month? Explain your answer."

Following is my answer. My question for the forum is, how did I do? Do you think this is a good explanation? Would you have been briefer? How so?

Answer: "Most of the homes are priced low, with only a few having higher prices bumping up the mean. And the mode only represents about half of the prices. There is relatively little variety between most of the prices, so the median better represents what the prices of the majority of the houses are."

I wouldn't change a word of it.

Originally Posted by Euclid Alexandria

Hello, I found this forum through a nearly abandoned Usenet group. Here are prices for 10 homes. The problem at hand asked me to find the mean, median and mode of these housing prices.

$120,000 $122,000 $125,000 $125,000 $139,000
$145,000 $167,000 $210,000 $540,000 $950,000

Answer: The mean average is $264,300. The median is $142,000. The mode is $125,000.

The problem then asked "Which measure of "average" best describes the average housing price for the month? Explain your answer."

Following is my answer. My question for the forum is, how did I do? Do you think this is a good explanation? Would you have been briefer? How so?

I recommend that you be more specific in your analysis:

80% of the houses are priced below the mean; the prices of the other two are more than 2 and 4 times as much as the 3rd highest priced house, skewing the mean into a misleading representation of the average price. The mode, however, is on the lower end of the prices, so it is not a reliable indicator of average costs either. There is relatively little variety among most of the prices, so the median best represents what the prices of the majority of the houses are.

What do you (all) think about possibly dismissing some of the higher values as outliers and then looking at the average?

Just a thought.

That is a very impressive suggestion, CTE. I hadn't previously thought of looking at averages like that. For some reason I had it in my head that the best average would always account for all numbers in a set, but now I see that means can be misleading.

Guru, interestingly, when I removed the three higher values, both the median and mode became the same, $125,000.

The mean became $134,714, which is closer to the other averages than the previous mean, which is $129,586 more.

Doing it this way seems to make the answer easier, but I don't think my math book was expecting me to dismiss prices. Is this generally permissible in classrooms?

There is a method for deciding whether values can be considered outliers.

This is only ten values or so so it may be difficult but check out these pages on detecting outliers:

http://www.graphpad.com/articles/outlier.htm

http://www.netnam.vn/unescocourse/statistics/37.htm

I think it is better to stick with your previous analysis. But the outlier thing may be a useful bit of statistics to familiarize yourself with.