2 1 frequency table

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  • 1. 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
  • 2. Frequency Table
    • A list of classes of values and the count of the actual values that occur in each class.
    • Favorite subjects of three Algebra 1 classes
      • Qualitative data
    53 Total 8 Music and arts 4 Science 15 Physical education 2 Languages 9 Social Studies 11 English 4 Math
  • 3. Let’s Build a Frequency Table: Page 572
    • M&M Colors
    Frequency Category
  • 4. Frequency Table
    • Average temperature for August 2009 and 2010
      • Qualitative data
    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. Characteristics of a Good Frequency Table
    • Class are mutually exclusive (no overlaps)
    • Together the classes include all possible (or practical) values.
      • Sum of all frequencies equals the number of original values
      • Includes classes whose frequency is 0
    • Convenient or sensible class limits
    • The frequency counts include the whole sample (or population)
    • Consistent class widths
      • “Greater than” or “Less than” classes sometimes necessary
    • Between 5 and 20 classes
  • 6. Definitions
    • Lower class boundary (LCB) :
      • The smallest value in each class
    • Upper class boundary (UCB) :
      • The largest value in each class
    • Class boundaries :
      • The midpoint (average) of the LCB and UCB of adjacent classes
    • Class midpoints :
      • The midpoint within a class. The average of a classes LCB and UCB
    • Class width :
      • the difference between the LCB of adjacent classes
  • 7. Building a quantitative frequency table
    • Estimate the number of classes
    • Calculate class width:
      • Round if convenient
    • Pick the LCB for the first class.
      • Minimum value
      • Round if convenient
    • Continually add the class width to the LCB of one class to get the LCB of the next.
    • Calculate the UCB
    • Tally the actual values in each class
  • 8. Let’s Build a Frequency Table: Page 573 Frequency Category
  • 9. Others
    • Relative Frequency Table
      • Each class lists its percent of total rather than the actual count
    • Cumulative Frequency Table
      • Each class lists the total frequency counts from the first class to the current class
      • Start with the “lowest” class
    • Relative Cumulative frequency Table
      • Each class lists the total percent of total from the first class to the current class
  • 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. Your turn: Let’s Build a Frequency Table Relative/ Cumulative Relative Cumulative Frequency Category
  • 12. Using Frequency Tables
    • Validating data
      • Does the frequency differ from what we would expect?
    • Exploring data
      • Spotting trends
      • Identifying “hot spots”
    • Comparing data
      • Changes over time
      • Comparing samples
  • 13. Two-way Frequency Table
    • Multiple categories for qualitative data
    • Day of the week is the row data
    • Gender is the column data
    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. Two-way Frequency Table
    • The sum of the rows and columns are called the marginal frequencies
    • Marginal frequencies are often expressed as percents
    • The marginal frequencies are usually graphed in a bar chart
    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. Conditional Relative Frequency
    • Calculating relative frequencies within a category
    • What percent of females like Monday?
    • What percent of Friday fans are male?
    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. Homework
    • Using your class data poll, create frequency and relative frequency tables for:
    • Favorite color
    • Favorite month
    • Using your class data poll, create frequency, relative frequency, and cumulative frequency tables for:
    • Math and CR SAT scores
    • Lucky numbers less than 100
  • 17. Gender
  • 18. By Favorite Day
  • 19.
    • Do male and females like different days
  • 20.  
  • 21.