Reading Graphs & Charts: PSAT/NMSQT Practice Problems

Line graphs and histograms are two of the most common visual formats on the PSAT/NMSQT Math section, and both test the same core skill: pulling accurate numerical information out of a picture and reasoning about it correctly. Line graphs typically track a quantity over time, and PSAT questions built around them ask about the rate of change between two points, which interval shows the steepest change, or projecting a future value using a percent change that mirrors an earlier trend. Histograms, on the other hand, display how data is distributed across ranges, or "bins," and PSAT questions often ask you to identify statistics — like the median — that can only be estimated within a range, not read off exactly.

The trickiest part of histogram questions is usually the median, because a histogram doesn't show individual data values — only how many values fall into each bin. To find the median, you have to count through the bins in order, keeping a running total, until you find the bin that contains the middle value (or values, if there's an even number of data points) of the entire data set. The correct answer is often expressed as "which of the following could be the median," meaning any value inside the correct bin is valid, not just one exact number.

Below are 4 PSAT/NMSQT-style practice problems using a line graph and a histogram, covering rate of change, percent change projections, and locating a median from grouped data. Work through each problem, select your answer, and check whether you got it right — every problem includes a complete, step-by-step explanation. Once you've worked through these, keep building your skills with thousands more official-style questions in our free PSAT/NMSQT Math QBank.

Questions 1–3 refer to the following information. The line graph below shows the enrollment for College R between 1950 and 2000.

Identifying the steepest interval on a line graph

According to the graph above, College R showed the greatest change in enrollment between which two decades?

Full Explanation

The "greatest change" corresponds to the steepest segment of the line — the segment that rises or falls the most vertically over one 10-year interval.

Reading the approximate values at each decade: 1950 ≈ 4, 1960 ≈ 3.5, 1970 ≈ 5.2, 1980 ≈ 5.8, 1990 ≈ 6.5, 2000 ≈ 7.

Compute the change for each decade: 1950–1960: about −0.5. 1960–1970: about +1.7. 1970–1980: about +0.6. 1980–1990: about +0.7. 1990–2000: about +0.5.

The change from 1960 to 1970 is by far the largest in magnitude, matching the steep upward segment on the graph. The correct answer is B.

Average rate of change over the full graph

What is the average rate of increase in enrollment per decade between 1950 and 2000?

Full Explanation

An average rate of change ignores the ups and downs in between and only compares the starting and ending values. Enrollment was about 4,000 in 1950 and about 7,000 in 2000.

Total change: 7,000 − 4,000 = 3,000 over the full span from 1950 to 2000.

That span covers (2000 − 1950)/10 = 5 decades. Average rate per decade: 3,000 / 5 = 600.

The correct answer is B.

Projecting forward using a matched percent change

If enrollment increases by approximately the same percentage between 2000 and 2010 as it decreased between 1950 and 1960, what is the expected enrollment in 2010?

Full Explanation

First find the percent decrease from 1950 to 1960, using the graph's approximate values of 4,000 (1950) and 3,500 (1960):

(4,000 − 3,500)/4,000 = 500/4,000 = 0.125 = 12.5% decrease

Apply that same percentage as an increase to the 2000 enrollment of 7,000 — not the same raw amount, since percent changes scale with the base value:

7,000 × 1.125 = 7,875

The expected enrollment in 2010 is 7,875. The correct answer is D.

Keep the momentum going.

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Finding the median from a histogram

The histogram below shows the distribution of the number of triples hit by 30 major league baseball teams in a certain year. Which of the following could be the median number of triples represented in the histogram?

Full Explanation

With 30 data points (teams), the median is the average of the 15th and 16th values when all the data is sorted in order. Find which bin those two middle values fall into by counting a running total through the bins in order.

Bin 10–20 has 3 teams (running total: 3). Bin 20–30 has 14 teams (running total: 3 + 14 = 17).

Since the 15th and 16th values fall between the 4th and 17th team counted, and that range is entirely covered once we reach the 20–30 bin, both the 15th and 16th values must fall inside the 20–30 bin.

The median must be a value between 20 and 30 (a histogram doesn't reveal the exact values within a bin, only the count). Checking the choices, only 19, 32, and 34 fall outside that range — 27 is the only choice that could be the median.

The correct answer is B.

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