Data Interpretation is Really About Reading Carefully (Well, That and Percents!)

by Jen Dziura May 7, 2012

While problems with charts and tables can look intimidating, it is often the case that the questions simply require you to be able to 1) read carefully, 2) do arithmetic, and 3) convert fractions to percents, and calculate percent change. That’s it.

Try this Data Interpretation problem set with five questions.

Ninth-Grade Students at Millbrook High School

1. What fraction of the girls are enrolled in Spanish?
2. What fraction of the students are boys who are enrolled in Spanish?
3. What is the ratio of 9^th grade girls not enrolled in Spanish to all 9^th grade students at Millbrook Middle School?
4. If x% more students are not enrolled in Spanish than are enrolled in Spanish, what is x?
5. If 2 of the boys not enrolled in Spanish decided to enroll in Spanish, and then 8 new girls and 7 new boys enrolled in the 9^th grade at Millbrook Middle School and also in Spanish, what percent of 9^th grade students at Millbrook would then be taking Spanish?

Record your answers on paper before continuing!

Solutions:

First, read the title of the chart: everyone accounted for in the chart is a ninth-grader at Millbrook Middle School. So, when problems mention 9th grade, you don’t have to figure out how many people involved are ninth graders ” everyone in the chart is.

When given a chart that depends on addition (boys plus girls = total students and those enrolled in Spanish plus those not enrolled in Spanish also = total students), it can be helpful to sketch a quick version of the chart on your paper and to add a total column. (If the chart is large and this would be too time-consuming, just imagine that the Total row and Total column are present, and only calculate what you need.) For example:

Now add down and across:

1. There are 29 total girls and 13 are enrolled in Spanish. The answer is 13/29.
2. There are 60 total students and 12 boys enrolled in Spanish. The answer is 12/60, which reduces to 1/5. (Read carefully! What fraction of the students are boys who are enrolled in Spanish? is NOT the same as What fraction of the boys are enrolled in Spanish?)
3. There are 16 girls not enrolled in Spanish and 60 total students. The answer is 16/60, which reduces to 4/15.
4. 35 students are not enrolled in Spanish and 25 are. The question can be rephrased as, 35 is what percent greater than 25? Using the percent change formula (Percent Change = Difference / Original, multiplied by 100), the percent change is 10/25, or 2/5, multiplied by 100, which gives us 40%.
5. Sketch a new chart to reflect the changes. Switch 2 of the boys from “not enrolled” to “enrolled.” Then, add 8 new girls and 7 new boys to the “enrolled” groups, like this:

   

   Update the Total rows and columns as well. You will see that both Boys and Girls, as well as Enrolled in Spanish and Not Enrolled in Spanish, now add to a total of 75.

   What percent of 9^th grade students at Millbrook are now taking Spanish? Since 42 out of 75 students are enrolled in Spanish, enter 42/75 into your calculator, then multiply by 100 to convert to a percent. The answer is 56%.