Page 169 - Data Science class 10
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Figure below is an illustration of the relationship between samples and populations:


                                    Research is meant for                      But actually made
                                          this size                             on this amount


                                                           Random selection


                                                                                   Sample


                                         Popluation            Inference







                                 Parameter   μ                                    X  Statistic
                                   (Population mean)                             (Sample mean)


            For example, let's imagine you're interested in learning the median income of magazine subscribers in
            general—this is a population parameter. You draw a random sample of 100 subscribers and determine that their
            mean income is $27,500 (a statistic). You conclude that the population mean income μ is likely to be close to
            $27,500 as well. This example is one of statistical inference.
            Different symbols are used to denote statistics and parameters, as shown in the following table:


                                                       Sample Statistic   Population Parameter
                                 Mean                         x                     m

                                 Standard deviation           s                   sigma
                                 Variance                    s 2                 sigma 2

            The information obtained from the statistical sample allows statisticians to create hypotheses about the wider
            population. In statistical equations, population is usually denoted with an uppercase N while the sample is usually
            denoted with a lowercase n.

            3.4.2. Standard Deviation

            The standard deviation is the variation in the population that is inferred from the variation in the sample. When the
            standard deviation is divided by the square root of the number of observations in the sample, the result is referred
            to as the standard error of the mean.
            In statistics, probability is a very important tool. The nature of the two situations will show the differences between
            them.
            Problem 1: Assume a coin is “fair”. Question: If a coin is tossed 10 times, how many times will we get “tail” on the
            top face?
            Problem 2: You pick up a coin. Question: Is this a fair coin? Or, does each face have an equal chance of appearing?
            Problem 1 is a mathematical probability problem. Problem 2 is a statistics problem that can use the mathematical
            probability model determined in Problem 1 as a tool to seek a solution. The answer  to neither  question is
            deterministic.






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