I'm actually taking statistics this semester and every now and then my professor will play excerpts from a documentary about statistics. The weird things is... it's not nearly as boring as one might imagine. Using statistics in the right way can make any presentation better in my opinion - you just have to be sure to introduce statistical information in an interesting and engaging way.
The best time to use statistics is when you're doing an informational/descriptive/persuasive speech. These rely heavily on logos, which is definitely buttressed by statistics and facts. Not only do statistics give you credibility as a speaker, but they are useful for the audience. Facts rather than ideologies give audiences something almost tangible to take away from your speech. Also, statistics can be exemplified in a visual format, which is also useful for the audience. Whether you're using a standard pie chart or a histogram or whatever, visual representations of statistical information gives your audience something that is often neglected in speeches - facts. Facts allow people to make their own decisions about the content of your speech because regardless of the speakers analysis, the facts do a little bit of speaking for themselves. I hope I didn't miscommunicate what I was trying to say - bear in mind, I used the words "statistics" and "facts" synonymously though statistics are not infallible - a point to certainly consider both as a speaker and as a member of an audience.
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