Results 1 to 6 of 6

Math Help - Averages - explaining answers

  1. #1
    Junior Member Euclid Alexandria's Avatar
    Joined
    Oct 2005
    From
    Near Dallas, Texas
    Posts
    73

    Question 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."
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Site Founder MathGuru's Avatar
    Joined
    Mar 2005
    From
    San Diego
    Posts
    478
    Awards
    1

    Thumbs up Well put

    I wouldn't change a word of it.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2005
    Posts
    27
    Quote 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.
    Last edited by MathGuru; October 12th 2005 at 10:50 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Site Founder MathGuru's Avatar
    Joined
    Mar 2005
    From
    San Diego
    Posts
    478
    Awards
    1

    Lightbulb

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

    Just a thought.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member Euclid Alexandria's Avatar
    Joined
    Oct 2005
    From
    Near Dallas, Texas
    Posts
    73

    Thank you for the input, people.

    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?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Site Founder MathGuru's Avatar
    Joined
    Mar 2005
    From
    San Diego
    Posts
    478
    Awards
    1

    Lightbulb Detecting Outliers

    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.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Explaining modulus
    Posted in the Algebra Forum
    Replies: 6
    Last Post: March 6th 2010, 02:25 AM
  2. Explaining Change
    Posted in the Statistics Forum
    Replies: 0
    Last Post: November 10th 2009, 07:56 AM
  3. need explaining
    Posted in the Calculus Forum
    Replies: 5
    Last Post: January 7th 2008, 06:54 PM
  4. Replies: 5
    Last Post: September 2nd 2007, 01:35 PM
  5. Two quadratic problems that need explaining
    Posted in the Algebra Forum
    Replies: 5
    Last Post: June 23rd 2007, 11:07 PM

Search Tags


/mathhelpforum @mathhelpforum