Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
AP STATISTIC EXAM REVIEW I: EXPLORING DATA (20β30%) CHAPTER 2 REVIEW: DESCRIBING LOCATION IN A DISTRIBUTION DENSITY CURVES AND NORMAL DISTRIBUTIONS β’ Two ways of describing an individualβs location within a distribution are percentiles and π-scores. An observationβs percentile is the percent of the distribution that is below the value of that observation. To standardize any observation π₯, subtract the mean of the distribution and then divide the difference by the standard deviation. The resulting π§-score π₯ β ππππ π§= π π‘ππππππ πππ£πππ‘πππ says how many standard deviations π₯ lies above or below the distribution mean. We can also use percentiles and π§-scores to compare the location of individuals in different distributions. β’ A cumulative relative frequency graph allows us to examine location within a distribution. Cumulative relative frequency graphs begin by grouping the observations into equal-width classes (much like the process of making a histogram). The completed graph shows the accumulating percent of observations as you move through the classes in increasing order. β’ It is common to transform data, especially when changing units of measurement. When you add a constant π to all the values in a data set, measures of center (median and mean) and location (quartiles and percentiles) increase by π. Measures of spread do not change. When you multiply all the values in a data set by a positive constant π, measures of center, location, and spread are multiplied by π. Neither of these transformations changes the shape of the distribution. β’ We can describe the overall pattern of a distribution by a density curve. A density curve always remains on or above the horizontal axis and has total area 1 underneath it. An area under a density curve gives the proportion of observations that fall in an interval of values. β’ A density curve is an idealized description of the overall pattern of a distribution that smooths out the irregularities in the actual data. We write the mean of a density curve as π and the standard deviation of a density curve as π to distinguish them from the mean π₯Μ and the standard deviation π π₯ of the actual data. β’ The mean and the median of a density curve can be located by eye. The mean π is the balance point of the curve. The median divides the area under the curve in half. The standard deviation π cannot be located by eye on most density curves. β’ The mean and median are equal for symmetric density curves. The mean of a skewed curve is located farther toward the long tail than the median is. β’ The normal distributions are described by a special family of bell-shaped, symmetric density curves, called normal curves. The mean π and standard deviation π completely specify a Normal distribution π(π, π). The mean is the center of the curve, and π is the distance from π to the change-of-curvature points on either side. β’ All Normal distributions obey the 68β95β99.7 rule, which describes what percent of observations lie within one, two, and three standard deviations of the mean. AP STATISTIC EXAM REVIEW I: EXPLORING DATA (20β30%) β’ All Normal distributions are the same when measurements are standardized. If x follows a Normal distribution with mean π and standard deviation π, we can standardize using π₯βπ π§= π The variable z has the standard normal distribution with mean 0 and standard deviation 1. β’ You can use your calculator to perform Normal calculations quickly. β’ To perform certain inference procedures in later chapters, we will need to know that the data come from populations that are approximately Normally distributed. To assess Normality for a given set of data, we first observe the shape of a dotplot, stemplot, or histogram. Then we can check how well the data fit the 68β95β99.7 rule for Normal distributions. Another good method for assessing Normality is to construct a Normal probability plot. **CHAPTER 2 AP EXAM TIPS** β’ Normal probability plots are not included on the AP Statistics topic outline. However, these graphs are very useful for assessing Normality. You may use them on the AP exam if you wishβjust be sure that you know what youβre looking for (a linear pattern).