Graphics Interpretation: line graphs, bar and pie charts, scatter plots and curves

What the question type asks

Graphics Interpretation is one of the five question types GMAC lists for Data Insights. As the name says, the work is reading a graphic, and this lesson covers the common kinds: line graphs, bar charts, pie charts, scatter plots and distribution curves. GMAC states that for Data Insights questions with several parts, all parts must be correct to score. The checks on this page are single-answer multiple choice, one question each, so treat each of them as one part done carefully. What you have to supply is careful reading and a little arithmetic.

This page cannot show images, so each graph below is described in words or given as the data table behind it. That is no handicap: the first thing to do with any graphic is to turn the part you need into a few numbers on your scratch paper.

Read the frame before the data

Every graphic has a frame, and most errors are frame errors.

• Title and period. "Monthly subscribers, January to June" tells you each point is a level at a moment, not a monthly change.
• Axes and units. Is the vertical axis in units, thousands, percent or dollars? Does it start at zero? On a bar chart whose axis starts at 80, bars of 90 and 99 differ by 10% but look like a doubling.
• Gridlines and scale. Read a value against the nearest gridlines and interpolate; if the answer choices are close together, read carefully; if they are far apart, a rough read is enough.
• Legend. With two lines or grouped bars, check which series is which before you read either.

Line graphs and x/y graphs: levels and changes

A line graph shows levels. Questions usually ask about changes between points:

• Absolute change is a subtraction: later value minus earlier value.
• Percent change divides that by the earlier value. The steepest segment of a line has the largest absolute change, but not necessarily the largest percent change, because the base differs.
• Average rate of change between two points is the change divided by the time between them: the slope of the straight line joining them.

Bar charts: grouped and stacked

In a grouped chart the bars for each category stand side by side, and you compare heights. In a stacked chart each bar is a total and the segments are its parts: read a segment's size as the top of the segment minus the bottom, never as the height at its top.

Pie charts: shares need a total

A pie chart shows shares of one total. A share alone gives no amount; you need the total. With two pie charts of different totals, a category's share can fall while its amount rises. Always convert to amounts (share times total) before comparing across charts.

A share change is measured in percentage points. A category whose share goes from 10% to 15% gained 5 percentage points, which is a 50% increase in its share.

Scatter plots and trend lines

A scatter plot shows pairs of values, one point per case. The pattern gives the relationship: points rising to the right show a positive association, falling to the right a negative one, and a shapeless cloud little association. A trend line gives a predicted value for each $x$; a point above the line did better than predicted, a point below it did worse. "How far above" can be asked in units (actual minus predicted) or in percent of the prediction ($\frac{\text{actual} - \text{predicted}}{\text{predicted}}$). Association is not cause: a graphic alone cannot show that one variable drives the other.

Distribution curves

A curve can show how a quantity is distributed: the area under it between two values is the fraction of cases between them. For a normal (bell-shaped) distribution with mean $\mu$ and standard deviation $\sigma$, a standard rule of thumb holds:

Interval	Share of cases, about
$\mu \pm \sigma$	68%
$\mu \pm 2\sigma$	95%
$\mu \pm 3\sigma$	99.7%

Because the curve is symmetric, half of what lies outside an interval is in each tail. So about 16% of cases are more than one standard deviation above the mean, and about 2.5% more than two above it.

A routine for every graphic

Read the frame; name the quantity the question wants (level, change, share, amount, gap from trend); pull only the values you need into a short list; compute; and check the answer against the picture. If the graph shows a line rising steeply and your answer says it fell, a value was misread.