Statistics is used almost all the things we do in real life... If we are familiar with something, then that is nothing but collecting data about it and whatever we do about that depending on the data is nothing but an application of statistics. Sometimes this happens if assumptions of a statistical method are violated. For example, linear regression based on OLS estimation makes assumptions about the distribution of the variable you are trying to predict. It is also possible that a particular statistical measure isn't the best for understanding some situation. For example, average household income is heavily right skewed, which means median income is often more representative of a typical household income than the mean. Finally, sometimes statistics can be misrepresented due to incorrect sampling methods. One common mistake is to "sample on the dependent variable". For example, say a journalist is interested in how well a random set of 100 stocks performed over the past 20 years. If the journalist took a random sample of 100 stocks currently trading today, this would be incorrect and overstate returns due to "survivor bias". One would need to instead pull a sample of 100 random stocks that were trading 20 years ago, as some then might go bankrupt or merge under adverse circumstances, reducing the mean returns.

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I completely agree with your in depth analysis. You really do point out some of the most leading facts about the subject. Sometimes statistics can be misrepresented due to incorrect sampling methods. One common mistake is to "sample on the dependent variable". For example, say a journalist is interested in how well a random set of 100 stocks performed over the past 20 years. If the journalist took a random sample of 100 stocks currently trading today, this would be incorrect and overstate returns due to "survivor bias". One would need