GMAT

Sub Topics

Understanding Bar Graphs And Pie Charts Summarizing Categorical Data Using Tables How to Calculate Percent Increase With Relative Cumulative Frequency Tables What is a Two Way Table Make Estimates And Predictions From Categorical Data What is Quantitative Data Definition Examples What is a Histogram in Math Definition Examples What Are Center Shape And Spread How to Calculate Mean Median Mode Range Describing The Relationship Between Two Quantitative Variables Reading And Interpreting Line Graphs Making Estimates And Predictions Using Quantitative Data z Test Formula Example Binomial Distribution Definition Formula Examples Range of Values Definition Overview Data Abstraction Definition Example Types of Statistical Analysis How to Draw a Trend Line How to Find The Equation of a Trend Line

Main Topics

Lessons and MCQs

Select Test Select Question Types

GMAT: Statistical Analysis With Categorical Data
Reading And Interpreting Line Graphs

Watch this video lesson to find out how useful line graphs can be and how much information you can gain just from looking at one. Learn how you can apply that information in your own life to help you make better decisions.

Reading And Interpreting Line Graphs

Line Graphs

Line graphs are cool! They are cool to look at, and they provide so much useful information once you know how to read them. You know when you are looking at a line graph when you see a graph with a line connecting the data points. The line can be straight, or it can be curved, or it can look like a connect-the-dots line. Whatever the case, there is so much information to be gained from these graphs.

Reading a Line Graph

Let's look at the line graph below that shows us the number of correct math problems a particular friend of ours gets right in one minute over the course of a week. Our friend, Joe, is taking a timed math test every day for a week. He is given a minute to solve as many basic arithmetic problems as he can. At the end of the minute, his work is graded, and the number of correct answers is noted down. Let's see what information we can gather from the line graph that was produced from his results.

kkk

Line graph showing number of correct math problems per minute

We see that on day 1, the first day, Joe didn't do very well, with only 1 correct math problem. I see this by looking at the bottom x axis first to locate day 1, drawing an imaginary line straight up, and then looking to find where our actual line crosses the imaginary line for day 1. I find the point where they cross, and then I draw another imaginary line across to see where it hits on the y axis. I see that it hits the y axis at 1, so Joe only got 1 correct math problem.

I keep reading the graph to gain more information. I look at day 2. How many math problems did Joe get right that day? I see where my line crosses day 2, and I see that it is where the y axis equals 5, so Joe got 5 correct math problems on day 2. On day 3, Joe got 8 correct answers. Day 4, he got 15. Day 5, it is 22. Day 6, Joe got 34 correct answers. And at the end of the week, on day 7, Joe was able to get 50 correct answers in one minute. Now that we've read our graph, what kind of interpretations can we make about Joe?

Interpreting a Line Graph

Reading a bunch of mathematical information from a graph is kind of meaningless unless we can interpret that data. What do all the numbers we read from the graph tell us about Joe? Looking at the line, we see that it keeps getting higher and higher. That is good for Joe. We can see that as the line gets higher, Joe's number of correct answers also gets higher. That means that Joe is doing really well. He is progressing in his math ability every day. He started out a bit slow, but then he started understanding more quickly. We can see this by the way the line curves slightly upwards.

We can also make an interpretation of what may happen to Joe's mathematical ability if he keeps going. It would make sense for the line to keep following the same pattern of going up, so if Joe kept this up, he'd be able to do more math problems in a minute on day 8 and day 9. Whether this will happen, we can't be sure, but based on the information we have, it seems likely. We just can't say that it will definitely happen.

A Real World Line Graph

Now, let's look at how we can read and interpret a line graph from a real-world scenario. We will see how being able to read and interpret the data will help us in our decisions. The particular line graph below shows the cost of a cell phone plan that includes 250 minutes.

kkk

Line graph showing cost of cell phone plan

This particular cell phone plan includes 250 minutes per month along with unlimited texting. The basic cost of the plan is $40 per month. Now, I read my line graph and see that after 250 minutes, my cost rises with the number of minutes. I went from $40 for 250 minutes to $65 for 300 minutes. That's a lot of money!

I see that the cost gets higher and higher the more minutes I use, all the way to $115 for 400 minutes. Doing a little math, I figure out that for every 50 minutes I go over my 250 minutes, I have to pay $25 more. If I divide $25 by 50, I figure that for each minute over 250 minutes, I am paying $0.50. I don't want to pay that much for a minute of talking if I go over my allotted time for the month.

I stop and think about this for a minute. I have to think about how much I really use this cell phone. Will I use more than 250 minutes per month with the cell phone? 250 minutes per month works out to a little over 4 hours of talk time. Do I talk that much on the phone every month? Or, do I text more? I like the $40 a month cost, but how likely am I to go over the 250 minutes?

Answering these questions will help me decide whether I should take this plan or upgrade to the next higher plan. After some thought, I decide I will take this plan because I don't talk on the phone that much. Because I text more than I talk, this plan will work for me.