Lecture3.sec.1.3

# Lecture3.sec.1.3 - Lecture 3 Section 1.3 As I have...

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Lecture 3, Section 1.3 As I have mentioned before, if the overall pattern of a large number of observations is quite regular, we chose to describe it by a smooth curve called a density curve . A density curve is an idealized model for the distribution of a quantitative variable. A Density curve has the following properties: 1. Is on or above the horizontal axis. 2. The total area under the curve is 1. 3. The area under the curve and above any range of values is the relative frequency of all observations that fall in that range (probability of occurrence). 4. Because density curves are continuous distributions, the chance of any exact value occurring is 0; only a range of values has a frequency, a probability of occurring. The median of a density curve is the equal-areas point. The mean of a density curve is the balance point. The median and the mean are always equal on a symmetric density curve. We designate the mean of a density curve as μ and the standard deviation as σ , when we are dealing with the population. When we take actual observations of a sample , we distinguish the mean of the distribution of these observations as x and the standard deviation as s . Lecture 3, Section 1.3 Page 1

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are a particularly important class of density curves. These density curves are symmetric, unimodal, and bell-shaped. They have the following properties: They are all symmetric Their mean is equivalent to their median The standard deviation σ controls the spread of a normal curve. We can actually locate by eye on a normal curve. Changing the mean, μ , without changing standard deviation, , moves the normal curve along the horizontal axis without changing the spread. Changing the without changing changes only the spread of the normal distribution. The Normal density curve can be fully described by giving its mean, , and standard deviation, . The values and are parameters of the curve and the Normal curve is completely determined by and . Lecture 3, Section 1.3 Page 2
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Lecture3.sec.1.3 - Lecture 3 Section 1.3 As I have...

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