2 1 frequency table
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TRANSCRIPT
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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
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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
Math 4
English 11
Social Studies 9
Languages 2
Physical education 15
Science 4
Music and arts 8
Total 53
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Let’s Build a Frequency Table: Page 572
Category Frequency
• M&M Colors
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Frequency Table
• Average temperature for August 2009 and 2010– Qualitative data
Temperature 2009 2010
85 - 89 0 3
80 - 84 9 8
75 - 79 13 11
70 - 74 7 7
65 - 69 2 2
60 – 64 0 0
55 – 59 0 0
31 31
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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
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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
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Building a quantitative frequency table
1. Estimate the number of classes
2. Calculate class width:
– Round if convenient 3. Pick the LCB for the first class.
– Minimum value– Round if convenient
4. Continually add the class width to the LCB of one class to get the LCB of the next.
5. Calculate the UCB6. Tally the actual values in each class
max min
number of classes
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Let’s Build a Frequency Table: Page 573
Category Frequency
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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
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Let’s Build a Frequency Table
Category Frequency
Cumulative Relative Relative/
Cumulative
90 – 95 0
85 - 89 3
80 - 84 8
75 - 79 11
70 - 74 7
65 - 69 2
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Your turn: Let’s Build a Frequency Table
Category Frequency
Cumulative Relative Relative/
Cumulative
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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
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Two-way Frequency Table
• Multiple categories for qualitative data
• Day of the week is the row data
• Gender is the column data
Favorite day Female Male
Sunday 2 0
Monday 2 2
Tuesday 1 1
Wednesday 1 1
Thursday 0 0
Friday 17 23
Saturday 17 18
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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
Favorite day Female Male
Sunday 2 0
Monday 2 2
Tuesday 1 1
Wednesday 1 1
Thursday 0 0
Friday 17 23
Saturday 17 18
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Conditional Relative Frequency
• Calculating relative frequencies within a category
• What percent of females like Monday?
• What percent of Friday fans are male?
Favorite day Female Male
Sunday 2 0
Monday 2 2
Tuesday 1 1
Wednesday 1 1
Thursday 0 0
Friday 17 23
Saturday 17 18
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Homework
• Using your class data poll, create frequency and relative frequency tables for:
1. Favorite color
2. Favorite month• Using your class data poll, create frequency, relative
frequency, and cumulative frequency tables for:
1. Math and CR SAT scores
2. Lucky numbers less than 100
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Gender
0%
10%
20%
30%
40%
50%
60%
Female Male
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By Favorite Day
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
Sunday Monday Tuesday Wednesday Thursday Friday Saturday
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• Do male and females like different days
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0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Sunday Monday Tuesday Wednesday Thursday Friday Saturday
Female
Male
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0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Sunday Monday Tuesday Wednesday Thursday Friday Saturday
Male
Female