2 1 frequency table

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2 1 frequency table

  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. Frequency Table <ul><li>A list of classes of values and the count of the actual values that occur in each class. </li></ul><ul><li>Favorite subjects of three Algebra 1 classes </li></ul><ul><ul><li>Qualitative data </li></ul></ul>53 Total 8 Music and arts 4 Science 15 Physical education 2 Languages 9 Social Studies 11 English 4 Math
  3. 3. Let’s Build a Frequency Table: Page 572 <ul><li>M&M Colors </li></ul>Frequency Category
  4. 4. Frequency Table <ul><li>Average temperature for August 2009 and 2010 </li></ul><ul><ul><li>Qualitative data </li></ul></ul>31 0 0 2 7 13 9 0 2009 0 60 – 64 31 0 2 7 11 8 3 2010 65 - 69 55 – 59 70 - 74 75 - 79 80 - 84 85 - 89 Temperature
  5. 5. Characteristics of a Good Frequency Table <ul><li>Class are mutually exclusive (no overlaps) </li></ul><ul><li>Together the classes include all possible (or practical) values. </li></ul><ul><ul><li>Sum of all frequencies equals the number of original values </li></ul></ul><ul><ul><li>Includes classes whose frequency is 0 </li></ul></ul><ul><li>Convenient or sensible class limits </li></ul><ul><li>The frequency counts include the whole sample (or population) </li></ul><ul><li>Consistent class widths </li></ul><ul><ul><li>“Greater than” or “Less than” classes sometimes necessary </li></ul></ul><ul><li>Between 5 and 20 classes </li></ul>
  6. 6. Definitions <ul><li>Lower class boundary (LCB) : </li></ul><ul><ul><li>The smallest value in each class </li></ul></ul><ul><li>Upper class boundary (UCB) : </li></ul><ul><ul><li>The largest value in each class </li></ul></ul><ul><li>Class boundaries : </li></ul><ul><ul><li>The midpoint (average) of the LCB and UCB of adjacent classes </li></ul></ul><ul><li>Class midpoints : </li></ul><ul><ul><li>The midpoint within a class. The average of a classes LCB and UCB </li></ul></ul><ul><li>Class width : </li></ul><ul><ul><li>the difference between the LCB of adjacent classes </li></ul></ul>
  7. 7. Building a quantitative frequency table <ul><li>Estimate the number of classes </li></ul><ul><li>Calculate class width: </li></ul><ul><ul><li>Round if convenient </li></ul></ul><ul><li>Pick the LCB for the first class. </li></ul><ul><ul><li>Minimum value </li></ul></ul><ul><ul><li>Round if convenient </li></ul></ul><ul><li>Continually add the class width to the LCB of one class to get the LCB of the next. </li></ul><ul><li>Calculate the UCB </li></ul><ul><li>Tally the actual values in each class </li></ul>
  8. 8. Let’s Build a Frequency Table: Page 573 Frequency Category
  9. 9. Others <ul><li>Relative Frequency Table </li></ul><ul><ul><li>Each class lists its percent of total rather than the actual count </li></ul></ul><ul><li>Cumulative Frequency Table </li></ul><ul><ul><li>Each class lists the total frequency counts from the first class to the current class </li></ul></ul><ul><ul><li>Start with the “lowest” class </li></ul></ul><ul><li>Relative Cumulative frequency Table </li></ul><ul><ul><li>Each class lists the total percent of total from the first class to the current class </li></ul></ul>
  10. 10. Let’s Build a Frequency Table 2 65 - 69 7 70 - 74 11 75 - 79 8 80 - 84 3 85 - 89 0 90 – 95 Relative/ Cumulative Relative Cumulative Frequency Category
  11. 11. Your turn: Let’s Build a Frequency Table Relative/ Cumulative Relative Cumulative Frequency Category
  12. 12. Using Frequency Tables <ul><li>Validating data </li></ul><ul><ul><li>Does the frequency differ from what we would expect? </li></ul></ul><ul><li>Exploring data </li></ul><ul><ul><li>Spotting trends </li></ul></ul><ul><ul><li>Identifying “hot spots” </li></ul></ul><ul><li>Comparing data </li></ul><ul><ul><li>Changes over time </li></ul></ul><ul><ul><li>Comparing samples </li></ul></ul>
  13. 13. Two-way Frequency Table <ul><li>Multiple categories for qualitative data </li></ul><ul><li>Day of the week is the row data </li></ul><ul><li>Gender is the column data </li></ul>18 17 Saturday 23 17 Friday 0 0 Thursday 1 1 Wednesday 1 1 Tuesday 2 0 Male 2 Sunday 2 Female Monday Favorite day
  14. 14. Two-way Frequency Table <ul><li>The sum of the rows and columns are called the marginal frequencies </li></ul><ul><li>Marginal frequencies are often expressed as percents </li></ul><ul><li>The marginal frequencies are usually graphed in a bar chart </li></ul>18 23 0 1 1 2 0 Male 17 Saturday 17 Friday 0 Thursday 1 Wednesday 1 Tuesday 2 Sunday 2 Female Monday Favorite day
  15. 15. Conditional Relative Frequency <ul><li>Calculating relative frequencies within a category </li></ul><ul><li>What percent of females like Monday? </li></ul><ul><li>What percent of Friday fans are male? </li></ul>18 23 0 1 1 2 0 Male 17 Saturday 17 Friday 0 Thursday 1 Wednesday 1 Tuesday 2 Sunday 2 Female Monday Favorite day
  16. 16. Homework <ul><li>Using your class data poll, create frequency and relative frequency tables for: </li></ul><ul><li>Favorite color </li></ul><ul><li>Favorite month </li></ul><ul><li>Using your class data poll, create frequency, relative frequency, and cumulative frequency tables for: </li></ul><ul><li>Math and CR SAT scores </li></ul><ul><li>Lucky numbers less than 100 </li></ul>
  17. 17. Gender
  18. 18. By Favorite Day
  19. 19. <ul><li>Do male and females like different days </li></ul>

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