It all depends of course on what the value(s) of that last observation happen to be, but it's just one observation, so it would need to be crazily out of the ordinary in order to change my statistic of interest much, which, of course, is unlikely and reflected in my narrow confidence interval. 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Divide the sum by the number of values in the data set. It is a measure of dispersion, showing how spread out the data points are around the mean. Imagine census data if the research question is about the country's entire real population, or perhaps it's a general scientific theory and we have an infinite "sample": then, again, if I want to know how the world works, I leverage my omnipotence and just calculate, rather than merely estimate, my statistic of interest. Adding a single new data point is like a single step forward for the archerhis aim should technically be better, but he could still be off by a wide margin. It's also important to understand that the standard deviation of a statistic specifically refers to and quantifies the probabilities of getting different sample statistics in different samples all randomly drawn from the same population, which, again, itself has just one true value for that statistic of interest. The steps in calculating the standard deviation are as follows: For each value, find its distance to the mean. $$\frac 1 n_js^2_j$$, The layman explanation goes like this. if a sample of student heights were in inches then so, too, would be the standard deviation. Standard deviation also tells us how far the average value is from the mean of the data set. For a data set that follows a normal distribution, approximately 68% (just over 2/3) of values will be within one standard deviation from the mean. (You can also watch a video summary of this article on YouTube). For a data set that follows a normal distribution, approximately 99.9999% (999999 out of 1 million) of values will be within 5 standard deviations from the mean. When the sample size increases, the standard deviation decreases When the sample size increases, the standard deviation stays the same. There are different equations that can be used to calculate confidence intervals depending on factors such as whether the standard deviation is known or smaller samples (n. 30) are involved, among others . Here is an example with such a small population and small sample size that we can actually write down every single sample. Sample size of 10: She is the author of Statistics For Dummies, Statistics II For Dummies, Statistics Workbook For Dummies, and Probability For Dummies. 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