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501_Lecture_01-3

501_Lecture_01-3 - Section 1.3 The Normal Distributions...

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Section 1.3 The Normal Distributions
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Topics Density curves Normal distributions The 68-95-99.7 rule The standard normal distribution Normal distribution calculations Standardizing observations Normal quantile plots
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Density curves
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Density curve Imagine a smooth curve thru the top of the bars on a histogram: it is an idealized mathematical model for the data Curve lies on or above the horizontal axis (non-negative) Has area exactly = 1 underneath it. Area under this curve for a given range give an estimate of the chance of an observation falling in that range Let’s look again…
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Density curves
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Definitions Mode Location where the curve is high-peaked Median the equal-areas point. Half the area on each side. Mean the balance point of the density curve Think of placing a wedge so that the density would balance like on a see-saw or teeter totter Hard to visually find the mean for skewed curves Mathematical formulas are used to calculate the mean, median, standard deviation, etc.
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Normal Density Curve
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A right skewed density curve
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Mean is the balance of the density curve
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Symbols μ mean of the idealized distribution (of the density curve) σ
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