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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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