Reading graphs and tables — Digital SAT Math practice
Extract and compare data from bar graphs and tables.
Key terms
- Axis: The reference lines on a graph that define the horizontal and vertical directions for plotting data values.
- Scale: The interval or increment marked along an axis that determines how much each unit or tick represents.
- Truncated Axis: An axis that starts at a value other than zero, which can visually exaggerate differences between bars or points.
- Data Point: A specific coordinate or cell entry representing a measured quantity in a graph or table.
- Standard Deviation: Measures data spread by taking the square root of variance, written as √(variance value).
Common traps
- Ignoring axis labels and units leads to misreading values by factors of ten or confusing counts with percentages.
- Comparing raw bar heights instead of the actual quantities when axes are truncated creates false impressions of magnitude.
- Calculating percent change using the new value as the denominator reverses the ratio and yields an incorrect percentage.
- Assuming a linear trend from two plotted points without checking intermediate data can produce wrong predictions.
Key ideas to know
Reading Axis Labels and Scales
A bar graph shows annual sales from 2020 to 2023. The vertical axis is labeled "Sales ($ thousands)" and starts at 40, increasing by 10 per grid line. If the 2022 bar reaches the third line above 40, what were the actual sales?
$70,000. Multiply the scale increment (10) by the number of lines from the axis start (3), add to the starting value (40), then apply the unit ($ thousands).
Watch out: Assuming the bottom grid line equals zero or ignoring the axis unit multiplier when calculating final values.
Matching Question Quantity to Data Type
A table shows Company A earned $5M profit on $50M revenue, and B earned $3M on $20M. The question asks which had a higher profit margin. Should you compare dollars or calculate percentages?
Calculate percentages (profit divided by revenue). Profit margin is a rate/percent, not a raw count. Comparing $5M to $3M ignores the different revenue bases.
Watch out: Choosing the larger dollar amount when the question asks for a rate or percent, ignoring that the totals differ.
Truncated Axes Exaggerate Differences
A bar graph compares test scores: Group X is 78, Group Y is 80. The vertical axis starts at 75, making bars look nearly equal. A student claims the difference is negligible because the bars are almost the same length. What is wrong?
The reasoning is flawed because a truncated axis distorts visual comparison. Trust the numerical values, not bar heights. The actual difference remains 2 points regardless of scale.
Watch out: Trusting visual bar heights over actual numerical values when the axis does not start at zero.