pam2100 handout_1_3 - 1.3 Density Curves and Normal...

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1.3 Density Curves and Normal Distributions Density Curve •idealized description of data distribution •smooth approximation to the irregular bars of a histogram Density Curve •The curve is always on or above the horizontal axis. •The curve has area exactly 1 underneath it. • The area under the density curve and above any range of values is the proportion of all observations that fall in that range.
Measuring center and spread for density curves mode - a peak point of a curve median - the point with half the total area on each side mean - the balance point (point at which curve would balance if made of solid material) •symmetric density curve→ mean and median are same •skewed distribution pulls mean towards its tail 2
A density curve is an idealized description of a distribution of data. We need to distinguish between the mean and standard deviation of the density curve and the numbers x and s computed from the actual observations. The usual notation for the mean of an idealized distribution is μ (the Greek letter mu). We write the standard deviation of a density curve as σ (the Greek letter sigma). Normal Distributions normal curves - symmetric, unimodal, and bell-shaped normal curves describe normal distributions all normal distributions have same overall shape exact shape for normal curve is defined by distributions μ and σ Figure 1.26 change μ→ move along horizontal axis increase σ→ increase spread σ is natural measure of spread for normal curve

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