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AP Statistics

Learn how to calculate the mean, median, and mode and understand when to use each measure of center. Explore the range, percentiles, and interquartile range. Identify outliers and construct boxplots. Calculate variance and standard deviation. Understand the effects of linear transformations on measures of center, spread, and the 5-number summary.

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AP Statistics

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  1. AP Statistics Section 1.2 Describing Distributions Numerically

  2. Objective: To be able to calculate the mean and median and know when it is appropriate to use each. Measures of Center: • Mean: average • Median: M It is the middle observation of a sorted data set. The median is located in the position. • Mode: the observation that occurs most often. (never more than 2 modes) • Midrange:

  3. When to use each measure of center: • Use the mean is the distribution is symmetrical. • Use the median if the distribution is skewed or outliers are present. • Use the mode when interested in greatest frequency. • Use the midrange when the data constantly fluctuates. Resistant refers to a statistic that is NOT affected by outliers. Which measures of center are resistant? Example: Find the measures of center for the Pulse Rate data.

  4. If the distribution is symmetrical, then the mean ______ median. If the distribution is skewed right, then the mean ______ median. If the distribution is skewed left, then the mean ______ median.

  5. Measures of Spread: • Range: max – min (resistant or nonresistant?) • Percentiles: Example: Given the following data set: 2,3,4,4,6,7,8,8,8,11 What percentile is 3? What percentile is 8? Special percentiles: 25th percentile: 75th percentile:

  6. Interquartile Range: (IQR) The range of the middle 50% of the data. Is the IQR resistant or nonresistant? Rules for Outliers: An observation will be considered an outlier if it lies above the upper cutoff point or below the lower cutoff point. Upper cutoff (fence) = Lower cutoff (fence) = Example: Are there any outliers in the pulse rate data set?

  7. Boxplots: graph used to relate the data to percentiles. Begin with the 5 Number Summary: Min, , Med, , Max • The whiskers extend to the smallest or largest observation that lies within the cutoff points Example: Construct a boxplot of the pulse rate data. ** Challenging Boxplot questions**

  8. Variance: the average of the squared deviations from the mean. Deviation: Always sum to ________ • Problem: Variance is measured in square units. • Standard deviation: the square root of the variance.

  9. Example: Find the variance and standard deviation for the following 5 bowling scores: **Standard deviation questions

  10. A linear transformation changes the variable X into a new variable Y by the equation Y=a+bX. Example: Find all measures of center, spread and the 5 number summary when X = the age of your dog. Let Y = 7X. (b = 7) What affect does multiplication have on all measures of center, spread and the 5 number summary?

  11. Let Y = -2 +7X. (a = -2) What affect does addition have on all measures of center, spread and the 5 number summary? Example: If we convert lunch prices from dollars to pesos using the following linear transformation, Y = 2+3X, give the new statistics in terms of Y. mode = _________ __________ IQR = 4 IQR = __________

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