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Thread: Variance and standard deviation. z-scores?

  1. #1
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    Variance and standard deviation. z-scores?

    Hi I have an exam this friday. Covering normal frequency distribution chart/graph, variance, standard deviation, and z-scores?

    So my question is there is that formula for standard deviation/variance. the s or s^2 is when we are using data from a sample and then on the bottom the formula will be /n-1 . on a population we use thetta or thetta^2, and N on the bottom only.

    My question is to get variance we just plug in data value + mean, and we get the variance in the square root. then if we square it, we get the standard deviation.

    What does variance mean on a chart or in practical use.

    Doesn't standard deviation represent the z-scores, in that, the middle will be 34.1 percent x2, which equals 68.2 percent of 1 standard deviation of the graph, then the next will be 13.1, which is 26.2, which 26.2+68.2, is 2 standard deviation, then the rest are considered outliers, or "unlikely"? So I could see what that means with data value.

    However, standard deviation is practically just dispersion of the data? How far apart we are from the next section or group? What does the variance do then? Also, how do I correlate standard variation with z-scores on a graph?
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  2. #2
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    Re: Variance and standard deviation. z-scores?

    Hey math951.

    The variance is an idea of how much variation there is and the variation roughly gives us an idea of the information contained in a distribution relative to some sort of parameter or quantity.

    In statistics, we take a sample and try and estimate things from that sample and the variance of the test statistic (which is used to do the estimation) gives us an idea of how confident we are that the estimate we make is in all likelihood - the actual value.

    We can get it right or wrong - we can get the right answer or do a false positive or false negative.

    The variance is inversely related to the information and it means that if you have more information in a sample then the variance of the test statistic used to make a guess about something common to all of the sample elements will be smaller and smaller and as it goes to zero, you get an idea of the actual value with more certainty.

    That is the most general way to look at variance and although it's not the only way to look at it - it does provide some sort of way to make sense of what it means beyond that of just a Normal distribution.
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    Re: Variance and standard deviation. z-scores?

    I apologize for digging up this post but it's related to my follow-question:

    Without knowing what the data measures, can we compare the variance of "different experiments" and meaningfully conclude that one data set has a greater variation than another (i.e., a data set from one experiment (e.g., dog height in mm) is more spread out than the data set from another, totally unrelated experiment (e.g., average height of a building in Manhattan in inches)?)
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