Statistics is quantative analysis tool and therefore only looks a general trends for patterns such as the correlation between two things (such as crime and poverty) with out examining the minutiae of individuals experiences.
The other form of analysis is qualitative research, which would comprise things such as case studies, observations or in-depth interviews with the group being analysed.
Also statistics can show a link between two things with out finding out which causes which.
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There are both advantages and disadvantages of data collection methods in statistics. The main advantages are the metrics and correlation one can draw from statistics. The disadvantages stem from sampling errors.
There are many advantages and disadvantages of variance in statistics. One disadvantage is that you never know what answer you'll get.
the mean is affected by outliers
Descriptive statistics are very useful for showing and summarizing data when any complex models are nit needed. However, it does not explain the relationship between two or more pieces of data and it does not leave any room to explain randomness in the data.
The advantages of using weighted averages are that it smooths out fluctuations due to statistical outliers. The disadvantage is that this gives a uniformity in the statistics and can make it difficult to project trends.