5.3 Reading Tables, Bar Graphs & Pie Charts for Trend Conclusions

What IOS Says These Items Look Like

The IOS study guide describes the NCJOSI² inductive reasoning items in one sentence: you will be given tables of information, bar graphs or pie graphs and asked to make general conclusions based on them. It frames the questions as "What trends do you notice? Have specific strategies been successful or unsuccessful?"

IOS's sample shows a grouped bar graph titled Number of Calls Received Daily, with one bar per week (Week 1, Week 2 and Week 3) for each weekday from Monday to Friday. Its two sample questions ask:

1. When were the fewest calls received? (a single smallest value)
2. Which day of the week saw the largest increase between Week 1 and Week 3? (the biggest difference between two series)

The bars you compare and the arithmetic you need are simple. Most errors come from reading the wrong bar, the wrong week or the wrong direction of change. The method below prevents that.

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The Five-Step Reading Order

Use the same order on every table or graph, before you look at the answer choices:

1. Title: What is being counted, and over what period? (calls per day, burglaries per quarter, percent of arrests)
2. Units: Are values raw counts, percentages, dollars or rates per 1,000 residents? Never mix units in one comparison.
3. Axis scale: Where does the vertical axis start, and what is the interval between gridlines? A bar graph that starts at 4,000 instead of 0 makes small differences look huge.
4. Legend: Which color or shading is which series (Week 1, Week 2, District A)? Point at the legend, then at the bar.
5. The question's exact comparison: Is it asking for a largest value, a smallest value, a largest increase, a decrease, a total or a share?

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Worked Example 1: Grouped Bars and "Largest Increase"

Suppose a bar graph shows traffic-crash reports for one city over two months. Read off the values into a quick table:

• Most crashes in a single bar: Friday in April (66).
• Fewest crashes in a single bar: Tuesday in March (38).
• Largest increase from March to April: Tuesday (+14), even though Tuesday never has the tallest bar.
• Only decrease: Wednesday (−4).

The trap here is choosing Friday for "largest increase" because Friday's bars are tallest. Height and change are different questions.

Percentage Change

Some items ask for a percentage increase. Use the original value as the denominator:

$\text{Percent change} = \frac{\text{New} - \text{Old}}{\text{Old}} \times 100$

Tuesday: $\frac{52 - 38}{38} \times 100 \approx 36.8\%$. Thursday: $\frac{58 - 50}{50} \times 100 = 16\%$. Tuesday has both the largest raw increase and the largest percentage increase here, but that is not always true: a small base can produce a large percentage from a small raw change.

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Worked Example 2: Pie Charts

A pie chart shows how one total is divided. Suppose a pie chart shows the 1,200 calls for service handled by one shift in a month:

Typical questions and how to answer them:

• "How many theft calls were there?" $0.20 \times 1{,}200 = 240$.
• "How many more traffic calls than alarm calls?" $(30\% - 15\%) \times 1{,}200 = 0.15 \times 1{,}200 = 180$.
• "Which two categories together make up more than half of all calls?" Traffic + Disturbance = 55%.

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Worked Example 3: "Was the Strategy Successful?"

IOS specifically mentions questions about whether strategies were successful. The key is comparison. Suppose a table shows residential burglaries before and after a foot-patrol program:

What the data supports:

• Burglaries fell in both program districts by a larger percentage than in the district without the program.
• District A had the largest drop in both count (−36) and percentage (−30%).

What the data does not support:

• "The program caused the drop." Other changes could explain it; one year of numbers shows association, not proof.
• "Burglaries will keep falling next year." The table says nothing about the future.
• "District C's program failed." Its burglaries still fell more than District B's, just less than District A's.

The best answer to a strategy question usually sounds like the first list: specific, comparative and no stronger than the numbers allow.

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Common Errors on Table and Graph Items