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Section 2.1 Density Curves & the Normal Distributions AP Statistics Berkley High School/CASA Density Curve “Mathematical Models” The area under the curve is related to the distribution of values “Idealized description” AP Statistics, Section 2.1, Part 1 2 Density Curves Characteristics Always above the x- axis Area always equal to 1 The area under the curve and above any range of values is the proportion of all observations that fall in that range. AP Statistics, Section 2.1, Part 1 3 Median and Mean Since the area represents portions of the population, the Median is the spot where the area to the left is the same as the area to the right. AP Statistics, Section 2.1, Part 1 4 Median and Mean The Mean represents the “balance point”. Imagine a “see-saw” AP Statistics, Section 2.1, Part 1 5 Median and Mean The Mean is always pulled towards the tail in a skewed distribution AP Statistics, Section 2.1, Part 1 6 “Idealized Distributions” We use different notation for density curve x mean of a sample (which represent s standard deviation of a sample entire populations) mean of a population as compared to data sets (which standard deviation of a population represent samples) AP Statistics, Section 2.1, Part 1 7 AP Statistics, Section 2.1, Part 1 8 AP Statistics, Section 2.1, Part 1 9 AP Statistics, Section 2.1, Part 1 10 Normal Distribution A special, bell shaped, symmetric, single-peaked distribution AP Statistics, Section 2.1, Part 1 11 Normal Distribution Because of the symmetry, the mean and median are the same and at the line symmetry AP Statistics, Section 2.1, Part 1 12 Normal Distribution The inflection points (where the curve starts to flatten out) represent the width of the standard deviation μ-σ AP Statistics, Section 2.1, Part 1 μ μ+σ 13 68-95-99.7 Rule AP Statistics, Section 2.1, Part 1 14 68-95-99.7 Rule with N(64.5,2.5) AP Statistics, Section 2.1, Part 1 15 Assignment Exercises 2.1 – 2.15 odd, The Practice of Statistics AP Statistics, Section 2.1, Part 1 16