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Describing, Exploring, and Comparing Data <ul><li>Summarizing  a set of data with a… </li></ul><ul><ul><li>Tables </li></u...
Summarizing data: Measures of Center <ul><li>Or measures of central tendency </li></ul><ul><li>Mean </li></ul><ul><ul><li>...
Mean <ul><li>Sum of the values divided by the number of values </li></ul><ul><li>Sample mean: </li></ul><ul><li>Population...
Mean: For example 1300 990 990 SAT 1300 1290 1190 1100 1050 1500 1200
Weighted Mean <ul><li>The values in a list vary in importance aside from their actual number </li></ul><ul><ul><li>E.g., i...
Weight Mean: For example Weight 1300 990 990 SAT 1300 1290 1190 1100 1050 1500 1200
Mean from a Frequency Table <ul><li>To calculate the mean from a frequency table </li></ul><ul><li>Find the class’s midpoi...
Median <ul><li>Then preferred measure of center when there are outliers </li></ul><ul><li>The middle value of an  ordered ...
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 <ul><li>Consider the following test scores: </li></ul><ul><li>92 81 75 84 77 81 79 70  </li></ul><ul><li>M...
Mode <ul><li>The most common value </li></ul><ul><li>Maybe none (if every value in the list is unique), one, or several </...
Midrange <ul><li>The value midway between the minimum and maximum values in the list </li></ul>1440 1390 1310 990 1300 126...
Live example <ul><li>Calculate the four measures of center </li></ul>72 82 86 86 80 90 74 58 28 58 88 98
Your Turn <ul><li>Calculate the four measures of the following data (Daily low temperature for Burlington, Vt for January ...
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2 4 measures of center

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Transcript of "2 4 measures of center"

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