# Reading Tables and Drawing Conclusions

Charts and tables are convenient ways to organize data.  The chart below organizes data about students by class and the science class they take.

 AP Biology AP Chemistry Total Sophomores 5 2 7 Juniors 23 16 39 Seniors 19 13 32 Total 47 31 78

What can we learn from a chart?

From the edges of the table, we learn totals.

The ends of the rows tell us the total numbers of Sophomores (7), Juniors (39), and Seniors (32).

At the bottoms of the columns we learn the total number of students who take AP Biology (47) and AP Chemistry (31).

Perhaps the most important cell of any chart is the bottom right hand corner, where the row and column totals meet, tells you the total number of datapoints in the table.  This table represents 78 students.

From the center of the table, we can learn how the categories overlap.  For instance, the totals tell us that there are 7 sophomores and that 47 students are taking AP Biology. But, the cell where "Sophomores" and "AP Biology" cross shows us that 5 sophomores are taking AP Biology.  The next cell down tells us that 23 juniors are taking AP Biology.

What can we do with data from a chart?

Because a chart gives us totals and subgroups, we can figure out what proportion or percent of the total group (or of a total subgroup) is part of another subgroup.  From that information, you can also figure out the probability that a member of one subgroup (or the entire group) will be a member of another subgroup.

Percents, proportions, and probability all rely on a simple fraction: $\dfrac{\text{Number that we care about}}{\text{Total number}}$.  So, to find a percent you are interested in, take the number you are interested in, put it over the total, divide, and turn the resulting decimal (proportion) into a percent (by dividing by 100).

Example:

What is the percentage of seniors who are taking AP Chemistry?

Number we care about: seniors in chemistry: 13

Total: seniors: 32

Fraction: $\dfrac{13}{32}=.40625=40.625%$

Example 2:

What is the probability that a randomly chosen student is enrolled in AP Chemistry?

Number we care about: students in AP Chemistry: 31

Total: students: 78

Fraction: $\dfrac{31}{78}$

Example 3:

What is the probability that a randomly chosen sophomore is enrolled in AP Biology?

Number we care about: sophomores in AP Biology: 5

Total: sophomores: 7

Fraction: $\dfrac{5}{7}$

Tables are not only used for probabilities.  They are also used to find descriptive statistics about a dataset.  A table is just a way to display data, so of course, you can also use the data in a table to find measures of central tendancy and other measures about data.  Let' look at that table again:

 AP Biology AP Chemistry Total Sophomores 5 2 7 Juniors 23 16 39 Seniors 19 13 32 Total 47 31 78

What if we wanted to find the average number of students from each class who took AP Biology?  What could we do?  First we write out our datapoints:

How many students in each class took AP Biology?  5 sophomores, 23 juniors, and 19 seniors.  What is the average number of students from each class?

$\dfrac{5+23+19}{3}=\dfrac{47}{3}=16.67 \text{ students from each class}$

You can also pull mode or median from a table like this.  There are no modes here, but what is the median number of students from each class that took AP Chemistry?

First, pull the datapoints, there were 2 sophomores, 16 juniors, and 13 seniors.  The middle data point is 13.  So the median number of students from each class who took AP Chemistry was 19.

The key to answering questions based on tables is to understand what data is in the table and how it's organized, and then pull out the info that you need and do the math.

• ## Reading Tables and Drawing Conclusions

A teacher surveyed the students in the third grade about how many pets they owned.  The table below summarizes the data:

 Number of pets Frequency 0 5 1 18 2 17 3 4 4 3 5 1 6 1

Use the table above to answer the following questions:

1. How many third graders were surveyed?
2. What is the mode of the data?
3. What is the median of the data?
4. What is the mean of the data?
5. What is the range of the data?
6. What is the minimum of the data?
7. What is the maximum of the data?

A class of AP Physics students took the AP Physics exam (which is notoriously difficult!).  The table below summarizes the students' scores on the exam

 Score on AP Physics Exam Frequency 1 9 2 10 3 8 4 6 5 3

Use the table above to answer the following questions:

1. How many students took the exam?
2. What is the mode of the data?
3. What is the median of the data?
4. What is the mean of the data?
5. What is the range of the data?
6. What is the minimum of the data?
7. What is the maximum of the data?

• ## Reading Tables and Drawing Conclusions

Use the following table to answer questions 1-10.

The US Supreme Court has an opening for a new associate justice. The table below details the results of a poll given in March 2016 to fill that opening.

 Vote this yearon replacement Leave vacant and wait ALL 48% 37% Male 45% 45% Female 49% 34% 18-34 42% 34% 35-49 49% 32% 50-64 54% 36% 65 and over 43% 52% Democrats 78% 8% Independents 48% 30% Republicans 16% 70% Liberal 80% 13% Moderate 52% 30% Conservative 17% 69%

1. What group would most like to have a replacement justice this year?

2. What group would most like to wait to fill the Supreme Court seat?

3. Which group has the largest gap between the percentage of people who would like a vote this year and those who would rather wait?

4. Which group has the smallest gap between the percentage of people who would like a vote this year and those who would rather wait?