The name of this tactic provides one reason why this is (or can be) an effective introduction. Startling statistics do just that—they startle an audience and catch its attention, and should also encourage that audience to listen further as you present the context of the startling statistic. Long-time radio announcer Paul Harvey is well known for the catch phrase “And now, the rest of the story.” The same function should be at work here. When you startle the audience, you set them up to want to hear the “rest of the story.”
Be careful, though. Use of startling statistics requires that you do a number of things. First, make sure the statistic is accurate. Second, make sure the statistic is relevant to the topic of the speech. Startling an audience with an irrelevant statistic diminishes the speech and decreases your credibility. Third, make sure you then present “the rest of the story.” You need to place this startling statistic in the context of your speech so that everything fits together.
This speaker used an effective startling statistic to help introduce a speech on the dangers of computer pollution: