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Calculating Sample Accuracy

  1. Apr 4, 2007 #1
    Ok. I'm fairly new so go easy on me. I apologise if this is posted in the wrong section.

    Can someone point me in the right direction of being able to work out samples of a web poll. A web poll I did returned the following results for a sample of 40 people and spending habits of a particular item.

    Code (Text):
    Range       Poll    %
    $0 - $500   6   15.00%
    $501 - $800 6   15.00%
    $801 - $1000    6   15.00%
    $1001 - $1200   3   7.50%
    $1201 - $1500   2   5.00%
    $1501 - $2000   5   12.50%
    $2001 - $3000   7   17.50%
    $3001+      5   12.50%
    What I'd like to be able to figure out is:
    (1) what would be the average; and
    (2) How accurate my sample size is (eg., We can be 99% sure that the average is x with a +/- 5% error margin) <-- I hope that makes sense.

  2. jcsd
  3. Apr 6, 2007 #2


    User Avatar
    Science Advisor

    Brad, you make it hard for yourself by having access only to "binned" data, but especially so by having an "open bin" on the last category.

    You estimate the mean by summing the category centers times the relative frequencies, as in : 250 * 0.15 + 650 * 0.15 + 900 * 0.15 + 1100 * 0.075 + ...

    You'll have to just guess a category center on the last bin though. You can get a lower bound on the mean by taking it as 3001 but there is unfortunately no upper bound.

    I took the cat-center of the last bin to be 3600 (for no particularly good reason) and got a mean (average) of about $1530.

    There are a few ways you can estimate the standard deviation for the raw data, I estimated it to be about 1070. The standard deviation for the sample mean is estimated as the standard deviation of the raw data divided by the square-root of the sample size. So you get the estimate of :

    Std-dev = 1070/sqr(40), which is approx 170.

    You get a 95% confidence interval on the sample mean by going roughly +/- two standard deviations, so that's $1530 +/- $340 for a 95% confidence level.

    Remember however that all my calculations are a bit shaky from the fact that I had to guess a category center (3600) for the last bin. So take the results with a grain of salt.
    Last edited: Apr 6, 2007
  4. Apr 11, 2007 #3
    Thanks Uart,

    Thats great. I see what you mean about binned data, especially the open ended upper range of the last category. I'm still learning. This is handy to reference. I'm going to see if I can experiment with it a bit more for collecting better data and getting better results.

    Sorry this reply is belated...for some reason I wasn't alerted by email to your reply. Do I have to set something on the forum to be alerted by email? I just noticed I can set the Notification Type to an individual thread to : "Instant email notification" but is there a way you can make this the default?

    Thanks again.

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