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2 4 measures of center
 

2 4 measures of center

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    2 4 measures of center 2 4 measures of center Presentation Transcript

    • Describing, Exploring, and Comparing Data
      • Summarizing a set of data with a…
        • Tables
        • Pictures
        • A small set of numbers that describes the data’s
          • Center
          • Variation
          • Distribution
          • Outliers
      • Comparing summaries
        • Several different groups
        • Changes over time within the same group
    • Summarizing data: Measures of Center
      • Or measures of central tendency
      • Mean
        • AKA: arithmetic mean, average
        • The ‘definitive’ single value for characterizing a set of data.
      • Median
        • Middle value
      • Mode
        • Most common value(s)
      • Midrange
    • Mean
      • Sum of the values divided by the number of values
      • Sample mean:
      • Population mean:
    • Mean: For example 1300 990 990 SAT 1300 1290 1190 1100 1050 1500 1200
    • Weighted Mean
      • The values in a list vary in importance aside from their actual number
        • E.g., in a list of SAT scores, the seniors’ scores might be more important that the juniors
      • We quantify the importance for each value, call it w n
      • Our formula
    • Weight Mean: For example Weight 1300 990 990 SAT 1300 1290 1190 1100 1050 1500 1200
    • Mean from a Frequency Table
      • To calculate the mean from a frequency table
      • Find the class’s midpoints
      • Multiply by the frequency
      • Add the products
      • Divide by the total frequencies
      Total Midpoint Freq Classes 1 4 63 121 11 75-79 70-74 65-69 60-64 55-59
    • Median
      • Then preferred measure of center when there are outliers
      • The middle value of an ordered list of values
      • Represented with the notation “x-tilde”
      • If the number of items in the list is odd, the median is the middle number in the list.
      • If the number of items is even, there will be two values in the middle. the median is the average of the two.
    • Median Example 1440 1390 1310 1300 1260 1210 1210 1170 1100 1050 1440 1390 1310 990 1300 1260 1210 1210 1170 1100 1050
    • Mean vs. Median
      • Consider the following test scores:
      • 92 81 75 84 77 81 79 70
      • Mean:
      • Median:
    • Mode
      • The most common value
      • Maybe none (if every value in the list is unique), one, or several
      • Only measure of center to use for nominal data
        • E.g., M&M colors
    • Midrange
      • The value midway between the minimum and maximum values in the list
      1440 1390 1310 990 1300 1260 1210 1210 1170 1100 1050
    • Live example
      • Calculate the four measures of center
      72 82 86 86 80 90 74 58 28 58 88 98
    • Your Turn
      • Calculate the four measures of the following data (Daily low temperature for Burlington, Vt for January 2010
      -1 -4 -1 12 28 32 37 14 2 9 14 27 31 31 32 27 34 18 -3 1 17 -6 -3 16 27 21 10 15 17 17 9