Chapter1.3 - 1.3 The Normal Distribution Key Words in...

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1.3 The Normal Distribution Key Words in Section 1.3 Density Curve: Mean and Median of a Density Curve Normal Distributions: Z-Score and Standard Normal Distibution Many times we wish to perform more complex tasks and ask more complex questions of our data than a data set alone can do. sometimes we find it desirable to use mathermatical experessions or formula that approximate or model the data. One such model is to approximate a histogram by a smooth curve or function. This will eliminate lumpiness in the histogram caused by choices of class interval. This type of curve is called a density curve . Density Curve A density curve is a curve that is always on or above the horizontal axis and has total area exactly 1 underneath it.
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Figure 1.20 (a) The distribution of pH values measuring the acidity of 105 samples of rainwater, for Example 1.21. The roughly symmetric distribution is pictures by both a histogram and a density curve.
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Figure 1.22 (b) The distribution of the survival times of 72 guinea pigs in a medical experiment, for Example 1.21. The right-skewed distribution is pictured by both a histogram and a density curve.
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Example 1.22 Fig.1.23(a) 0.303 Fig.1.23(b) 0.293
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Relative frequency - the fraction or percent of the observations that fall in each class. From Example 1.22, the shaded area under the density curve in Fig. 1.23(b) is 0.293, only 0.010 away from the histogram result (0.303). A density curve describes the overall pattern of a distribution. The area under the curve and above any range of values is the relative frequency of all observations that fall in that range. The density curve in Figure 1.23 is a normal curve . Figure 1.24(a) A symmetric density curve with its mean and median marked
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Density curves, like distributions, come in many shapes. Figure 1.24(b)
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Chapter1.3 - 1.3 The Normal Distribution Key Words in...

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