earson Coefficient of Skewness A measure to determine the skewness of a distribution is called the Pearson coefficient of skewness (PC). The formula is PC =3−XMDs The values of the coefficient usually range from −3 to +3 . When the distribution is symmetric, the coefficient is zero; when the distribution is positively skewed, it is positive; and when the distribution is negatively skewed, it is negative. Using the formula, find the coefficient of skewness for each distribution and describe the shape of the distribution. Round your answers to two decimal places as needed. a) Mean =10 , median =11 , standard deviation =3 The coefficient of skewness is This distribution is (b) Mean =42 , median =41 , standard deviation =4 The coefficient of skewness is This distribution is (c) Mean =17.7 , median =17.8 , standard deviation =1.6 The coefficient of skewness is This distribution is (d) Mean =97 , median =96.5 , standard deviation =5 The coefficient of skewness is This distribution is
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!
Pearson Coefficient of Skewness A measure to determine the skewness of a distribution is called the Pearson coefficient of skewness (PC). The formula is
| PC |
=3−XMDs
|
The values of the coefficient usually
to
. When the distribution is symmetric, the coefficient is zero; when the distribution is positively skewed, it is positive; and when the distribution is negatively skewed, it is negative.
Using the formula, find the coefficient of skewness for each distribution and describe the shape of the distribution. Round your answers to two decimal places as needed.
a)
|
The coefficient of skewness is
This distribution is |
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(b) Mean =42 , median =41 , standard deviation =4
| The coefficient of skewness is
This distribution is |
(c) Mean =17.7 , median =17.8 , standard deviation =1.6
| The coefficient of skewness is
|
|
(d) Mean =97 , median =96.5 , standard deviation =5
|
The coefficient of skewness is
|
|
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