the mean x and standard deviation s measure center and variability but are not a complete description of a distribution. Data sets with diffrent shapes can have the same mean and standard deviation. to demonstrate this fact use your calculator to find x and s for these two small data sets. then make a stem plot of each and comment on the shape of each distributiondata a : 9.14 8.14 8.74 8.77 9.26 8.10 6.13 3.10 9.13 7.26 4.74data b : 6.58 5.76 7.71 8.84 8.47 7.04 5.25 5.56 7.91 6.89 12.50
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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data a : 9.14 8.14 8.74 8.77 9.26 8.10 6.13 3.10 9.13 7.26 4.74
data b : 6.58 5.76 7.71 8.84 8.47 7.04 5.25 5.56 7.91 6.89 12.50
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