***When analyzing two-way tables, you want to compare the relative frequencies (percentages) of the data instead of solely using the numbers in the table head to head.
For example: In this two-way table, it would be a mistake to generalize that more people who are younger than 18 watch the news daily because you are comparing 30 to 10. This generalization does not include the fact that different amount of people were surveyed.
Instead you could find the relative frequency of people who watch the news to find that 30/110 people younger than 18 watch the news daily, while 10/15 people 18 or older watch the news daily.
This shows that 27% of people younger than 18 watch the news daily while 67% of people 18 years or older watch the news daily.
Therefore there is an relationship between people being 18 or older and watching the news more frequently, whilepeople who are younger than 18 typically do not watch the news on a daily basis.
Relative Frequency: being asked to find the relative frequency is the same as finding the percent chance of that event happening.
STUDENT SUPERPOWER CHOICE
Researchers once surveyed students on which superpower they would most like to have. The following two-way table displays data for the sample of students who responded to the survey.
What percent of males chose invisibility as their superpower?
What percent of males chose other as their superpower?
What percent of students chose flight as their superpower?
HOW MUCH YOU MAKE AFTER COLLEGE
Researchers surveyed recent graduates of two different universities about their income. The following two-way table displays data for the sample of graduates who responded to the survey.
Approximately what percent of graduates in the sample came from University A?
Approximately what percent of graduates from University A make $40,000 and over?
STUDENTS PLAYING SPORTS AND INSTRUMENTS
Here is a two-way table that gives some results from the survey. Please complete the remainder of the table, so all the totals are correct.
To the nearest percentage point, what percentage of students who play a sport don’t play a musical instrument?
To the nearest percentage point, what percentage of students who don’t play a sport also don’t play a musical instrument?
TO RAISE MINIMUM WAGE OR NOT
A reporter in a small town polled some residents and asked them if they were in favor of increasing the minimum wage or against it. The two-way table summarizes the data.
Name two things you notice and two things you wonder about the table.
How many people did the reporter survey?
How many people in the age group of 16–30 years old were against the increase in minimum wage?
Were more people in favor of the increase or against the increase?
More people were in favor
More people were against the minimum wage increase
A random group of students are polled about how they get to school by walking, riding the bus, or carpooling.
Of the 44 male students polled, 9 of them walk and 26 of them ride the bus.
Of the 58 female students, 26 of them ride the bus and 24 of them carpool.
Create a two-way table to represent the data. Label your rows as Male and Female.
What is the percent of all of the students, who are female and walk to school?
Of the students who carpool, what percent are female?
A student is selected at random from this school. What would you predict this student’s mode of school transportation to be? Explain your answer
SEGMENTED BAR GRAPHS Questions
The graph below is a segmented bar graph. In order to create a segmented bar graph, you must find the relative frequency (percentage) of each row or column.
The Y axis (which is not labeled above) represents percent.
Estimate the percent of 10-12 year olds who have no cell phone.
Is there an association between age and having a cell phone, if so describe the association.
Complete the table below by filling in the relative frequencies of each row.
Using your frequency table from the previous problem, create your own segmented bar graph.
(look at the example of the segmented bar graph prior to problem 17 to see a visual)
*be sure each bar goes up to 100%
*be sure to include a key
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