Chapter_03 - Chapter 3 The Normal Distributions BPS - 5th...

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BPS - 5th Ed. Chapter 3 1 Chapter 3 The Normal Distributions
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BPS - 5th Ed. Chapter 3 2 Density Curves Example : here is a histogram of vocabulary scores of 947 seventh graders. The smooth curve drawn over the histogram is a mathematical model for the distribution.
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BPS - 5th Ed. Chapter 3 3 Density Curves Example : the areas of the shaded bars in this histogram represent the proportion of scores in the observed data that are less than or equal to 6.0. This proportion is equal to 0.303.
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BPS - 5th Ed. Chapter 3 4 Density Curves Example : now the area under the smooth curve to the left of 6.0 is shaded. If the scale is adjusted so the total area under the curve is exactly 1, then this curve is called a density curve . The proportion of the area to the left of 6.0 is now equal to 0.293.
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BPS - 5th Ed. Chapter 3 5 Density Curves Always on or above the horizontal axis Have area exactly 1 underneath curve Area under the curve and above any range of values is the proportion of all observations that fall in that range
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BPS - 5th Ed. Chapter 3 6 Density Curves The median of a density curve is the equal-areas point, the point that divides the area under the curve in half The mean of a density curve is the balance point, at which the curve would balance if made of solid material
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BPS - 5th Ed. Chapter 3 7 Density Curves The mean and standard deviation computed from actual observations (data) are denoted by and s , respectively. x The mean and standard deviation of the actual distribution represented by the density curve are denoted by µ (“mu”) and σ (“sigma”), respectively.
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BPS - 5th Ed. Chapter 3
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Chapter_03 - Chapter 3 The Normal Distributions BPS - 5th...

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