2 1 frequency table
- 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