Because it ensures the relevance of variation as significant due to inherent capacity or otherwise due to chance factor.
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The graph that is most used for categorical data is the pie chart. Bar graphs have also been used for categorical data.
Yes, the mode is the "most popular" score of an array. It is possible to find the mode for categorical data that has more than 2 responses to the question.
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Bar chart or bar graph
There are very many ways of analysing data and it is not possible to list them all. Furthermore, most techniques are appropriate only in certain circumstances and so the question needs to be more specific before it can be answered.