you find which one is best for example, the mode could be the beat because it shows the most amount of data. just by looking at the mode you can figure out a lot about the survey and the data you have collected.
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A weighted mean is probably best. Certainly better than a median which throws away information from most of the observations.
-- Circumference of the circle = (pi) x (radius) -- length of the intercepted arc/circumference = degree measure of the central angle/360 degrees
If you absolutely needed to measure an angle to find out its degree measure, you would use a protractor.
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It often gives us a way to find the measure of other angles.