Transcript Two Way Frequency Tables

Two Way Frequency Tables
Unit 2 Data Analysis – Two Way Tables
CCSS - What do we see?
S.ID. 1 Represent data w/ plots on the real number
line (dot plots, histograms, & box plots).
S.ID. 2 - Use statistics appropriate to the shape of
the data distribution to compare center (median,
mean) and spread (interquartile range, standard
deviation) of two or more different data sets
S.ID. 3 Interpret differences in shape, center, and
spread in the context of the data sets, accounting
for possible effects of extreme data points (outliers).
Key Vocabulary
Two-Way Table: categorical data organized in
2 dimensions
Class discussion
What’s the difference between a distribution of
heights and a distribution of favorite fast food?
Categorical Data: Data that can be organized in a
two-way table, counting the frequency of the
categories (such as fast food).
Numerical Data: Data that cannot be organized in
a two-way table. It needs a scaled axis (such as
heights).
Numerical (quantitative) data vs.
Categorical (qualitative) data
You and your partner:
1. Come up with ONE example of data not yet
mentioned
2. Decide whether each example is numerical
and/or categorical. Can a set of data be both?
Android vs. iPhone
-On ONE post-it, please write your name (first
and last).
-Stick it to the appropriate quadrant on the
whiteboard.
Android vs. iPhone
Android
Female
Male
Total
iPhone
Total
Do you see any trends (patterns in the data)?
• Discuss with your partner.
– Any patterns in the data?
– Can you find certain statistics, such as the mean?
Remember: We summarize categorical data for
two categories in a two-way frequency table
In our data, we might say there appears to be
an association (a relationship between two
measured quantities).
Answer the following questions with
your partner. Be prepared to share
with the class.
Using the class data, answer & discuss:
1. How many students total from this class prefer
the Android?
2. How many students prefer the iPhone?
3. How many students are females?
4. How many students are males?
5. How many students are females AND prefer the
Android?
6. How many students are males AND prefer the
iPhone?
Questions #1-6 are frequency questions about data.
Using the class data, answer & discuss:
7. What ratio (think fraction) are males AND
prefer iPhones?
8. What ratio of students are males AND prefer
Androids?
Questions #7-8
• These questions are questions of joint relative
frequency (the ratio of the value in the body
of the table, to the total).
Using the class data, answer & discuss:
9. What ratio of students prefer the iPhone?
What percent is this?
Question #9
• This question is a question of marginal
relative frequency (the ratio of the value of a
subtotal, to the total)
Using the class data, answer & discuss:
10.If we only look at the female students, what
ratio prefers the iPhone?
11. If we only look at students who prefer
Android, what proportion are male?
Questions #10-11
• These questions are questions of conditional
relative frequency (the ratio of the value in
the body of a table, to a subtotal)
Use the two-way table to answer the following question(s).
Example 1.
1. What is the ratio of the students who own a
cell phone and MP3 player?
(joint relative frequency)
2. What is the ratio of the students who own a
cell phone? (marginal relative frequency)
3. Out of the students who own a cell phone,
what is the ratio of the students who own an
MP3? (conditional relative frequency)
Create a two-way table to display the data,
and answer the following question(s).
Example 2. It was found that 70 students own headphones
and 22 students own LED TVs. There were 63 students that
do not own LED TVs. 11 students own both.
1. Of the students who own headphones, what is the ratio of
those who own LED TVs?
As a class, we will…
1. Select a topic to create a two-way table.
2. Complete the two-way table.
3. Come up with 3 questions on the given twoway table.
4. Answer the questions.
Class Data