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2 6 measure of position

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  • 1. Measure of Position
    • Looking at individual values: Where does it lie among the sample (or population)
      • standard score (or z score)
      • quartiles, deciles, and percentiles
    • 25%-75% SAT scores
      • Princeton 1370 – 1560
      • Villanova 1180 – 1340
  • 2. Standard Score (z score)
    • How many standard deviations from the mean is a sample?
    • Z scores less that –2.00 or greater that 2.00 are outliers.
  • 3. For example
    • 25 55 59 59 63 71 71 74 80 80 80 83 84 84 87 88 95 95 100 100
    • Mean : 77
    • Standard deviation = 18
    mean mean +  mean + 2  mean + 3  mean - 3  mean - 2  mean - 1 
  • 4. Quartiles
    • Separates the sorted list into four parts separated by three boundaries
    min lower quartile median max upper quartile 25% 25% 25% 25%
    • If the median separates the list into two halves
      • The lower quartile is the median of the lower half
      • The upper quartile is the median of the upper half
  • 5. For example
    • 25 55 59 59 63 71 71 74 80 80 80 83 84 84 87 88 95 95 100 100
  • 6. Deciles
    • 25 55 59 59 63 71 71 74 80 80 80 83 84 84 87 88 95 95 100 100
    min median max 10% 10% 10%
  • 7. Percentile
    • Percentile value of a value x
    • Where does x sit in a set of data
    • For example:
    • 25 55 59 59 63 71 71 74 80 80 80 83 84 84 87 88 95 95 100 100
    • What is the percentile of:
  • 8. Finding the value at the k th Percentile
    • n values in our sample
    • Data has to be sorted
    • Compute L, the position of the k th percentile
    • If L is a whole number, the percentile is midway between L and L+1
    • If L is a decimal, round up; the percentile is the L th value
  • 9. For example
    • 25 55 59 59 63 71 71 74 80 80 80 83 84 84 87 88 95 95 100 100
    • What is the value at the
  • 10. Relationships
    • The 1 st quartile is the same as the 25 th percentile
    • The 3 rd quartile is the same as the 75 th percentile
    • The first decile is the same as the 10 th percentile
  • 11. Live example
    • What are the mean and standard deviation
    • What are the minimum, lower quartile, median, upper quartile, and maximum
    • What is the 4 th decile
    • What is the 35% percentile?
    • What is South’s z value
    • What is South’s percentile?
  • 12. Your turn
    • What are the mean and standard deviation
    • What are the minimum, lower quartile, median, upper quartile, and maximum
    • What is the 4 th decile?
    • What is the 35% percentile?
    • What is Rob’s z score?
    • What is Rob’s percentile?