GMAT Exam: A Simple Guide To Arithmetic - Graphical Representation of Data

For the GMAT, be prepared to read and interpret information from frequency or relative frequency tables, pictographs, circle graphs, dot plots, stem-and-leaf plots, line graphs, bar graphs, and histograms.

Frequency Tables
A frequency table shows the frequency of each value in the data set. A relative frequency table shows the frequency as a proportion or percentage of the whole data set.

Here is an example.

Exam 1 Grade Distribution of 20 Students


According to the table, 0.40 + 0.30 + 0.15 = 0.85 or 85% of the students made a C or better on Exam 1.

Pictographs
A pictograph represents data with symbols (or images). Each symbol, its meaning, and the quantity it represents are given on the graph.

To read a pictograph, multiply the number of symbols in a row by the quantity it represents. If a fraction of a symbol is shown, approximate the fraction and use it accordingly.

Here is an example.

Responses of 200 Women to the Question “Do You Have a Sibling?”


According to the graph, 15 × 10 = 150 women responded “Yes” to the survey question.

Circle Graphs
A circle graph (or pie chart) displays the relationships of different categories of data as portions of a whole, represented by a circle. The portions are labeled to show the categories for the graph. Percentages show the amount of the graph that corresponds to each category.

Here is an example.

According to the graph 40% + 25% = 65% of the students are freshmen or sophomores.

Dot Plots
A dot plot (or line plot) shows the frequency of data values on a number line. Dots (or other similar symbols) are placed above each value corresponding to the number of times that particular value occurs in the data set.

Tip: A useful feature of dot plots is that they show all the data values.

Here is an example.


The dot plot shows three customers waited more than 15 minutes.

Stem-and-Leaf Plots
A stem-and-leaf plot visually displays data values, separated into two parts: a stem and a leaf. For a particular data value, the leaf is usually the last digit, and the stem is the remaining digits. A legend explains what is represented by the stem and leaf so that the reader can interpret the information in the plot; for example, 5|7 = 57.

Tip: A feature of a stem-and-leaf plot is that the original data are retained and displayed in the plot.

Here is an example.

According to the graph, five presidents were 54 years of age at the time of their inauguration.

Line Graphs
A line graph shows plotted points that represent data. Consecutive points are connected with line segments. The slant of the line between points shows trends in the data. A line that slants upward from left to right indicates an increase. A line that slants downward from left to right indicates a decrease. A horizontal line (no slant) means the data remain constant. Line graphs are commonly used to show change over time.

Here is an example.


The line graph shows an upward trend in average monthly sales from February to May.

Bar Graphs
A bar graph uses rectangular bars to represent frequencies, percentages, or amounts. The bars represent different categories that are labeled at the base of the bars. To read a bar graph, examine the scale to determine the units and the amount corresponding to each category.

Here is an example.


According to the graph, 40 males and 60 females are enrolled.

Histograms
A histogram summarizes data by displaying frequencies or relative frequencies of the data within intervals. The intervals are of equal length and cover from the lowest to the highest data value. The left and right endpoints for the intervals are selected so that each data value clearly falls within one and only one interval. The frequency or relative frequency of occurrence of the data values within an interval is represented by a rectangular (or vertical) column. The bars in a histogram are side by side (usually) with no space in between.

Here is an example.