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AP Statistics Chapter 1 & 2 – One Variable Statistics. Categorical variable places an individual into one of several groups or categories (p. 3) Quantitative Variable takes numerical values for which it makes sense to find an average (p. 3) Graphical Methods for one set of data. Dot plots (pp. 27-32) Pie and bar charts, segmented bar charts for categorical data (pp. 8-19) Histograms (pp. 35-39) Relative frequency histograms (see p. ) Cumulative relative frequency plots (see pp. 86-89) Stem and Leaf Plots (pp. 33-35) Box Plots (pp. 59-61) Graphical Methods comparing two sets of data. Parallel dot plots (see p. 32) Back to back stem and leaf plots (see p. 33-35) Parallel box plots (see p. 67) ALWAYS INCLUDE SCALES, LABELS, & a title on your graphs. Describing the shape of data. Section pp. 29-32 Terms included are positively skewed (right), negatively skewed (left), symmetric, uniform, approximately normal, bimodal, gaps & clusters and outliers. Describing the center of data. Section 1.3 Section 2.1 discusses the sample mean and median. Be able to calculate these measures of center. Property of mean. ( x x ) 0 The median is resistant to outliers. If the data is skewed left, the mean < median. If the data is skewed right, the median < mean. Be able to identify which measure of center is more appropriate given a data set. Describing the spread of data. Section 1.3 Section 1.3 discusses standard deviation, range, and interquartile range. Be sure to use the correct vocabulary, the range is a single value. Use the word spread when appropriate, not “range”. Range is a single value. Range = maximum – minimum. IQR = Q3-Q1 = Upper Quartile – Lower Quartile Be able to calculate standard deviation on your calculator. The standard deviation is a weighted average of the typical distance from the mean. Standard deviation is sensitive to outliers, IQR is not sensitive to outliers. Understand which measure of spread is more appropriate given the data. When describing a distribution, always describe the center, shape, spread in the context. Be able to calculator outliers Lower outliers < Q1 – 1.5(IQR) upper outlier > Q3 + 1.5(IQR). Section 2.1 This section also discussed percentiles; the rth percentile is a value such that r percent of the observations in the data set fall below that value. See pp. 85-89. Also discusses relationship between mean and median on skewed data. Discusses impact of adding or multiplying a data set by a constant. See pp. 94-95 x This section introduced z-scores. z . A z-score is the number of standard deviation the value is from the mean. Section 2.2: Normal Distributions This section introduced you to the 68-95-99.7% Rule. You should be able to calculate z-scores and probabilities using the chart or calculator command normalcdf(lowerbound, upperbound). You should be able to calculate a score x given a probability using the chart or invnorm(area to left) and then formula z . You must show work on free response questions. See p. 123 & 124 for more detailed calculator commands and examples. Normalpdf is used when you want to graph a normal curve. Normalcdf (lower bound, upperbound) is used when you want to find the probability when you now the z-score. Normalcdf (lower bound, upperbound, , ) is also an option if you have the original values. Invnorm(area to left) calculates the associated z-score. Invnorm(area to left, , ) calculates the associated data value if you enter the mean and standard deviation. Checking for Normality: (pp. 124-128) To determine if data is approximately normal, use the normal probability plot. If the normal probability plot is approximately linear, then the data is approximately normal. You must sketch the normal probability plot on the AP test and write the sentence above. AP Problems: 2002#3, 2007#3, 2009#2, 2004B#3, 2005B#6, 2008B#5, 2008B#5, 2000#6, 2006B#3