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# 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
• 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.