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  • 1. Describing Distributions with Numbers
  • 2. VOCABULARY
    • Mean – the average of all observations
    • Median – the middle number
      • Put numbers in order smallest to largest
      • If # of observations is odd, M is the center
      • If # of observations is even, M is the mean of the two center observations
  • 3. DIFFERENCES BETWEEN MEAN AND MEDIAN
    • Median is resistant to extreme observations
      • 3 5 8 10 14 17 100
      • Median = 10
    • Mean is not resistant to extreme observations
      • 5 8 10 14 17 100
      • Mean = 22.4286
  • 4. SPREAD OR VARIABILITY
    • Range – shows the full spread of the data
      • Largest value minus smallest value (outliers can change this value drastically)
    • Quartiles – marks out the quarters of the data (middle of the halves)
  • 5. QUARTILES
    • First Quartile – lies one-quarter of the way up the list of data.
    • Third Quartile – lies three-quarters of the way up the list of data.
  • 6. CALCULATING THE QUARTILES
    • Arrange the observations in increasing order
    • Locate the median M
    • The first quartile Q 1 is the median of the observations lying to the left of the overall median (not counting the median value)
    • The third quartile Q 3 is the median of the observations lying to the right of the overall median
  • 7. MORE WITH QUARTILES
    • IQR – the interquartile range is the distance between the first and third quartiles.
      • Used to determine if an observation is an outlier
      • Observation is called an outlier if it falls more than 1.5 x IQR below Q 1 or above Q 3 .
  • 8. FIVE NUMBER SUMMARY
    • Minimum
    • Q 1 (First Quartile)
    • Median
    • Q 3 (Third Quartile)
    • Maximum
      • This summary defines the boxplots.
  • 9. BOXPLOTS
    • Regular boxplot does not distinguish outliers
    • Modified boxplot distinguishes outliers by plotting them as points (use this one!!!)
  • 10. ASSIGNMENT
    • Page 34-36 #1.24 – 1.30
    • Page 37-42 #1.31 – 1.34
    • 1997 AP FR Q#1
    • 2001 AP FR Q#1
  • 11. STANDARD DEVIATION
    • Measures spread by looking at how far the observations are from the mean
      • Most common numerical method of describing spread
  • 12. VOCABULARY FOR STANDARD DEVIATION
    • Variance – the average of the squares of the deviations of the observations from their mean
    • Standard deviation (s) – the square root of the variance
    • (Note: The sum of the errors is zero!!!)
  • 13. EXAMPLE
    • Use the given data to answer the questions:
    • 1792 1666 1362 1614 1460 1867 1439
    • 1. Find the mean
    • 2. Find the variance
    • 3. Find the standard deviation
  • 14. EXAMPLE
    • Use the given data to answer the questions:
    • 1792 1666 1362 1614 1460 1867 1439
    • 1. Find the mean
    • 2. Find the variance
    • 3. Find the standard deviation
  • 15. PROPERTIES OF STANDARD DEVIATION
    • s measures spread about the mean and should be used only when the mean is chosen as the measure of center
    • s = 0 only when there is no spread. This happens only when all observations have the same value
    • s, like the mean, is strongly influenced by extreme observations (non-resistant)
  • 16. ASSIGNMENT
    • Page 43-47 #1.35 – 1.37
    • Page 48 #1.38, 1.41, 1.43, 1.46
    • Summary Statistics Worksheet
    • Prepare for Quiz 1.2