Read and interpret data from tables, bar graphs, line graphs, histograms, pie charts and box plots, and compute statistics or probabilities from a display (Statistics and Probability, Integrating Essential Skills).

What this topic is asking

The ACT presents data in many visual forms, tables, bar graphs, line graphs, histograms, pie charts and box plots, and asks you to read values and compute statistics, totals, fractions or probabilities from them. The skill is accurate reading of the display plus the right follow-up calculation.

Reading common displays

Each display answers a different question.

Computing from a display

Reading the scale correctly

The most frequent display error is misreading the scale. A bar graph axis might go up in steps of 5 or 50, not 1, so a bar reaching the third gridline could be 15, not 3. A histogram's bars represent ranges of values, so a bar over "10 to 20" counts everything in that interval, not a single value. Always check the axis labels and the value of one gridline before reading off numbers. A pie chart gives percentages, which you must multiply by the total to get an actual amount.

Box plots and the five-number summary

A box plot (box-and-whisker) displays five values: the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. The box spans Q1 to Q3 (the interquartile range, IQR $=$ Q3 $-$ Q1, the middle 50% of the data), with a line at the median; the whiskers reach the min and max. So a box plot lets you read the median and spread at a glance and compare two data sets' centres and ranges. The ACT may ask for the median, the range (max minus min), or the IQR directly from the plot.

Two-way frequency tables

A two-way table classifies data by two categories at once, for example students by grade level (rows) and by whether they play a sport (columns), with row and column totals in the margins. To read it, find the cell where the row and column meet; to find a probability, divide the relevant cell or total by the grand total. A conditional question ("of the seniors, what fraction play a sport?") divides by the row total for seniors, not the grand total. Keeping straight which total is the denominator, the whole group or a specific row or column, is the central skill for these tables, which the ACT uses often.

Comparing data sets from displays

Some questions show two displays, such as two box plots or two bar graphs, and ask you to compare. Compare centres (which has the higher median or mean), spread (which has the larger range or IQR), and shape (symmetric or skewed). A box plot whose median line sits further right has a higher median; a wider box has more spread in the middle 50%. Reading the comparison directly from the displays, rather than reconstructing the raw data, is what the ACT expects, and it rewards careful attention to the axis scale on both displays.

Why careful reading wins points

Data-interpretation questions are usually easy arithmetic once you read the display correctly. The reliable habit is to slow down on the labels, units and scale before computing, then apply the right statistic. Treating a pie-chart percentage as a count, or misjudging a gridline's value, are the errors that cost points; reading deliberately and converting percentages to amounts prevents them.

Try this

Q1. A pie chart shows 25% of a $1,600 budget goes to food. How much is that? [1 point]

• Cue. 0.25 \times 1600 = \400$.

Q2. A box plot shows min 4, Q1 7, median 10, Q3 14, max 20. What is the IQR? [1 point]

• Cue. IQR $=$ Q3 $-$ Q1 $= 14 - 7 = 7$.