# Reading Tables and Filling in Missing Data

Charts and tables are convenient ways to organize data.  Usually the trick to reading them is just paying close attention to labels.  A typical grid or table will have labels along one side and the top.  Each cell will contain a value that is unique to the value along the side and along the top.  So, a chart of fees for classes might list classes along the top and dates along the side.  If you want to find the cost of a Calculus class that is being held in June, you'd go across the top, find "Calculus," then go down until you reach the "June" row.  That cell, at the intersection of "Calculus" and "June" should show you the fees for the June Calculus class.

Many tables also contain "total" rows and columns.  These rows and columns are somewhat self explanatory: they contain totals.  Total cells that are at the ends of rows are "row totals": they total every item in that row.  Total rows at the bottom of columns are "column totals" and they contain the totals of each column. If there is a cell that is both a row total and a column total, then it should total both all the rows and all the columns (in other words, the total of the rows should equal the total of the columns and that total is in that bottom corner cell).

The table below shows "Students enrolled in AP Science, by class standing."  You can see that there are 5 sophomores enrolled in AP Biology and 2 sophomores enrolled in AP Chemistry.  The Sophomore row total shows that 7 sophomores are enrolled in AP science ($5+2=7$).  Likewise, you can look at the column total of AP Biology and see how many students (of any class standing) are enrolled in AP Biology: $5+23+19=47$.  There are 47 students total enrolled in AP Biology.  The number in the bottom right corner, 78, is the total of all the rows and the total of all the columns.  The total number of sophomores, juniors, and seniors enrolled in AP science (78) is equal to the total number of students enrolled in either AP Biology or AP Chemistry (78).

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

The trick to solving problems that give you a table and missing data in that table is understanding how the row and column totals work, and following the details in the question.

Let's look at the next table which shows a school's Athlete's academic status:

 Above 2.5 GPA Below 2.5 GPA Total Football 37 13 50 Men's Basketball 5 20 Women's Softball 27 13 Total 79 31 110

The table does not show how many students on the Men's Basketball team have above a 2.5 GPA.  How can you figure it out?  The row total shows that there are 20 students on the Men's basketball team.  The cell that shows how many Men's Basketball players have below a 2.5 GPA says 5 students.  So, you can subtract $20-5=15$.  There are 15 players on the men's basketball team who have above a 2.5 GPA!

Likewise, the table is missing the total number of Women's Softball players, but that's easy to find.  Just total the row: $27+13=40$.  There are 40 players on the Women's Softball team.

 Above 2.5 GPA Below 2.5 GPA Total Football 37 13 50 Men's Basketball $\color{red}{\text{15}}$ 5 20 Women's Softball 27 13 $\color{red}{\text{40}}$ Total 79 31 110

Sometimes these types of questions are a big more complicated, but follow the rules about row and column totals and read the question carefully and you should get them!

Example: The table below shows the amounts that Mark, Steve, and Susan spent on their new cars.  If they all spent the same amount for their cars (but different amounts for extra add-ons). How much did Mark spend all together?

 Car Cost Cost of Add-ons Total Mark \$125 Steve \$290 Susan \$48 Total \$22,963

The first thing you want to do is figure out what parts of the table you can fill in with the information given.

You can easily fill in the column total for add-ons: $125+290+48=463$

 Car Cost Cost of Add-ons Total Mark \$125 Steve \$290 Susan \$48 Total$\color{red}{\text{\$463}}$ \$22,963 From there, you can figure out the total Car Cost because you know the row total and the total cost of add-ons:$22,963-463=22500$.  Car Cost Cost of Add-ons Total Mark \$125 Steve \$290 Susan \$48 Total $\color{blue}{\text{\$22,500}}\color{red}{\text{\$463}}$ \$22,963 Now, you need to go back to the question for some more info. Mark, Steve, and Susan all spent the same amount on their cars. So, we take the column total of \$22,500 and divide it by 3: $22,500\div 3=7500$.  They each spent \$7500 on a car. Fill in that info, and then you can also fill in the row totals for each car buyer:  Car Cost Cost of Add-ons Total Mark$\color{green}{\text{\$7500}}$ \$125$\color{green}{\text{\$7625}}$ Steve $\color{green}{\text{\$7500}}$\$290 $\color{green}{\text{\$7790}}$Susan$\color{green}{\text{\$7500}}$ \$48$\color{green}{\text{\$7548}}$ Total $\color{blue}{\text{\$22,500}}\color{red}{\text{\$463}}$ \$22,963 What did the question ask again? How much did Mark spend? \$7625.

Overall, for these kinds of questions, just remember how to use row and column totals and you should be able to fill in the tables and find the answers!