Math · Problem-Solving and Data Analysis

One-Variable Data on the Digital SAT

One-variable data questions test whether you actually understand what mean, median, mode, range, and standard deviation say about a list of numbers, not just whether you can compute them. The Digital SAT rarely asks "find the mean" and stops. It asks what happens to the mean when one value changes, or which statistic an outlier drags around, or what a fifth test score must be to hit a target average.

The relationship between mean and median is the heart of this skill. The mean uses every value, so one extreme number can yank it far from the center. The median only cares about position, so it barely notices an outlier. Questions are built directly on that contrast, and the wrong answers are built for students who treat the two as interchangeable.

Standard deviation shows up conceptually, not computationally. You will never calculate one by hand. You just need to know it measures spread: data bunched near the mean has a small standard deviation, and data scattered far from the mean has a large one. With Desmos available for any arithmetic, these questions come down to reasoning, not calculation.

New to the Digital SAT? Start with how the test is structured and scored.

What the SAT actually tests

Computing and comparing mean, median, mode, and range for small data sets given in the question.
How adding, removing, or changing a value moves the mean versus the median.
Outlier effects: extreme values pull the mean and stretch the range but usually leave the median alone.
Standard deviation as a concept: which of two data sets is more spread out from its mean.
Working backwards from a mean, like finding the score needed on one more test to reach a target average.
Reading described distributions, such as data sets summarized in words or frequency counts.
Histogram interval reasoning, where each bar covers a range of values, so you can only pin the median to a bin, not a single value.

Strategies that work

Think in totals, not averages

The mean is just total divided by count, so convert every mean statement into a total immediately. Four tests averaging 82 means 328 points banked. A target average of 85 over five tests means 425 points needed. Now the question is simple subtraction instead of a fog of averages.

Sort before you touch the median

The median is the middle value of the sorted list, and the SAT will happily present data out of order. Rewrite the list in order first, even when it looks close to sorted. For an even count, the median is the average of the two middle values, which is another detail the answer choices will test.

Ask "who feels the outlier?"

When one value in a set becomes extreme, run down the statistics: the mean moves toward the outlier, the range stretches, the standard deviation grows, and the median usually stays put because the middle position has not changed. Most outlier questions are answered by this checklist alone, with no computation.

Compare spread by distance from the mean

For standard deviation questions, do not reach for a formula. Picture each data set and ask how far typical values sit from the center. A set like 10, 10, 11, 11 hugs its mean; a set like 1, 5, 16, 20 does not. The one with values farther from the mean has the larger standard deviation, and that comparison is all the SAT asks for.

Mistakes to avoid

Reporting the mean when the question asks for the median, or vice versa, since both are "averages" in casual speech.
Thinking the mode has to be a majority. The mode is just the single most-frequent value, so a value that shows up in only 30% of the data can still be the mode.
Assuming an outlier shifts the median as much as the mean, when the median usually barely moves.
Forgetting to re-sort the list after a value changes before finding the new median.
Answering a target-average question with the target itself, instead of the higher score needed to pull the average up.
Treating standard deviation as if it depends on the size of the values rather than their spread around the mean.

Solve it with Desmos

Let the calculator do the work

The Digital SAT's built-in Desmos calculator can crack One-Variable Data questions in a few clicks. Here is the move that applies, step by step.

Find Mean, Median, or Standard Deviation from a ListDump the numbers in, let a formula do the sorting.

All 15 Desmos techniques

Practice with Nova, your Math coach

Answer right here and Nova walks you through it, just like in a drill. Difficulty labels are relative within this skill.

Tip: the Calculator button on each question opens the same Desmos graphing calculator you get on the real Digital SAT. Try solving these with it.

Question 1Easy

A student asked five friends how many books each read over the summer and recorded the results in the dot plot shown.

Books Read over the Summer

What is the median of the data set shown in the dot plot?

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Question 2Medium

A data set consists of the values 2, 4, 5, 6, and 8. The value 8 is then replaced with 38, and no other values change.

Which statement correctly describes how the mean and the median of the data set change?

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Question 3Hard

After four tests, Ana's mean score is exactly 82. There is one test remaining, and all five tests are weighted equally.

What score must Ana earn on the fifth test so that her mean score for all five tests is 85?

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The rest of Problem-Solving and Data Analysis

One-Variable Data is one of 7 skills in Problem-Solving and Data Analysis. The ideas build on each other, so it pays to learn them as a set rather than in isolation. See how Problem-Solving and Data Analysis fits together.

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