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Average, Median and Fastest: Reading Your Response Time Numbers

Answer times are skewed, so the average is pulled up by a single long think. Here is what mean, median, fastest and consistency each tell you about a session.

By Published Updated 6 min read

Reign Creative LLC makes IQ Test & Brain Training Games, which this article links to, so we have a commercial interest in it. How we write and check articles.

Key takeaways

  • Answer times are not symmetrical. Response time distributions are reliably positively skewed, which means a small number of very slow answers sit far from the rest and drag the average upwards.
  • In a ten-answer example where nine times sit between 1.8 and 3.0 seconds and one stall takes 12 seconds, the mean is 3.30 seconds while the median is 2.35 seconds. The median describes the typical answer; the mean describes the stall.
  • National statistics agencies use the median rather than the mean for skewed data for exactly this reason, and the same logic applies to your own session record.
  • A fastest-correct figure is a single trial, so it is the noisiest number on the screen. It is a reasonable thing to enjoy and a poor thing to track.
  • Consistency usually improves before speed does, because the first thing practice removes is the occasional stall rather than the routine answer time.

Read the median, not the average. A session's average answer time is pulled upwards by the slowest one or two answers, while the median sits at the middle of the run and describes the answer you actually typically gave. The fastest-correct figure is a single trial and therefore the noisiest number you are shown, and a consistency figure describes variability rather than pace.

Those four numbers look like four measurements of the same thing. They are not, and knowing which is which changes what your practice record appears to say.

Answer times are skewed, and that is the whole problem

If you plotted every answer you gave in a session, the shape would not be a symmetrical hump. It would rise quickly, peak, and then trail off to the right with a long thin tail of slow answers.

This is not a quirk of arithmetic drills; it is how response times behave generally. The Frontiers in Psychology paper To transform or not to transform by Lo and Andrews describes response time distributions as "unimodal with a distinct positive skew" and notes that "the distribution of RTs obtained in simple decision tasks is invariably positively skewed". It also flags the practical consequence directly: "skewed RT data can affect the estimate of the mean, thus distorting the outcome of statistical tests", with the risk that "just a few extreme outliers might dominate the outcome".

The asymmetry has an intuitive cause. There is a floor on how fast you can answer — you cannot read, compute and tap in under some minimum — but no ceiling on how slow one answer can be. Lose your place, reconsider a carry, or get distracted, and a single item can take five times your usual.

The same session, two numbers

Here is a made-up but realistic run of ten answer times, in seconds, from a short arithmetic round:

1.8, 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.7, 3.0, 12.0

The mean is the total divided by ten. The times add to 33.0 seconds, so the mean is 3.30 seconds.

The median is the middle of the sorted list. With ten values there is no single middle, so it is the average of the fifth and sixth: 2.3 and 2.4, giving 2.35 seconds.

Now change one thing. Suppose the 12-second stall had instead been an ordinary 2.6-second answer. The times then total 23.6 seconds, so the mean becomes 2.36 seconds — a drop of almost a full second. The median moves from 2.35 to 2.35: it does not move at all.

That is the entire argument. One item changed the mean by 0.94 seconds and the median by nothing. If your goal is a number that tracks your typical answer, the median is the one that does the job; if your goal is to notice that you stalled once, the gap between mean and median is the signal, and it is more informative than either number alone.

National statistics agencies make the same choice for the same reason. The Office for National Statistics explains in its housing affordability bulletin that the median "is a more useful measure of an average than the mean where a distribution is skewed, as is the case with both income and house prices". Household income and arithmetic answer times have nothing else in common, but they share the shape, and the shape is what decides which average to use.

What "fastest correct" is actually good for

A fastest-correct time is the single quickest right answer in a run. It is a nice thing to see and a bad thing to track, for a reason that has nothing to do with your ability: it is an extreme value drawn from one trial, so it is dominated by luck about which question you happened to be asked.

An easy item in a mixed set — a doubling, or a fact you happen to have rehearsed that morning — will produce a fast time regardless of whether your arithmetic improved. Across weeks, a fastest-correct series is mostly a record of how many easy questions you were dealt.

Where it is genuinely useful is as a floor check. If your median is four seconds and your fastest correct is 0.9 seconds, you know the ceiling on your input speed is not the constraint; the time is going on computation, and a method change could help. If median and fastest are close together, you are already near the mechanical limit of tapping answers in and further speed gains are small.

Consistency: the number that moves first

IQ Test & Brain Training Games is our own app — Reign Creative builds it — and alongside average, median and fastest-correct it records a consistency value on a nought-to-one-hundred scale, described in the app as how consistent response times were across the run.

That number deserves attention because it usually improves before pace does. The first effect of practising a method is not that your ordinary answers get faster; it is that the occasional catastrophic answer stops happening. You still take about two seconds on a familiar item, but you no longer take twelve on the one that used to derail you.

On a record, that shows up as: median roughly flat, mean falling, consistency rising. Read only the median and it looks like nothing happened. Read only the mean and it looks like you got faster across the board, which is not what occurred. Read the three together and you get the true story — the tail is shrinking.

This is also why a plateau in one number is not a plateau overall. Why practice scores stop improving works through the other readings of a flat curve.

Comparing two sessions without fooling yourself

Timing numbers are only comparable when the thing being timed is the same, and that is easier to get wrong than it sounds.

  • Same mode. A mixed-operation round includes a decision step that a single-operation sprint does not, so its times are structurally longer. That is a property of the task, not of you.
  • Same difficulty. Two-digit by two-digit questions take longer than single-digit ones by design. Comparing across difficulty labels measures the label.
  • Same length. A longer round includes more fatigued answers, and fatigue lengthens the tail. Sustained-task performance declines with time on task, which is one reason how long a brain training session should be matters for the record as well as for the practice.
  • Alongside accuracy. Speed and accuracy trade against each other — Heitz's review of the speed-accuracy tradeoff calls the covariation "an inescapable property of choice behavior" — so a faster median with lower accuracy is a strategy change, not an improvement. Accuracy before speed covers the order to train them in.

One further caution: a single session is a small sample. Ten answers give a median that can shift by a couple of tenths on noise alone. Look at the direction across four or five comparable sessions rather than the difference between yesterday and today.

What these numbers are not

Response times recorded by a drill app are timings of that app's questions on your device, including the time it takes to read the screen and tap. They are not reaction times in the laboratory sense, they are not comparable to any published norm, and they do not measure processing speed as a psychological construct. There is no assessment happening in a drill round — it reports statistics about its own questions and nothing else. Our app's separate reaction time test and IQ-style test are a different feature, and its listing describes their results as estimates based on app activities, not clinical or professional assessments.

Used for what they are, they are genuinely useful: a way to see whether a method has become automatic. The rest of the practice-record articles sit in the brain training games hub, the honest limits of the whole category are covered in do brain training apps work, the app itself is described on the IQ Test & Brain Training Games app page, and more of this writing is collected in the education and brain category.

Good to know

Frequently asked questions

Should I track average or median response time?
Track the median. Answer times are positively skewed, so a handful of long thinks pull the mean well above the time most of your answers actually took. The median sits at the middle of your answers and moves only when your typical answer changes, which is what you want a progress number to do.
Why is my average answer time so much higher than it feels?
Because one or two stalls dominate it. If nine answers take about two seconds and one takes twelve, the twelve-second answer contributes more to the mean than any other single item. Your sense of the session comes from the nine ordinary answers; the mean is mostly reporting the one unusual one.
What does a consistency figure tell me?
It summarises how much your answer times vary within a run rather than how fast they are. Two sessions with the same median can look very different: one steady, one alternating between instant recall and long reconstruction. Rising consistency with an unchanged median usually means stalls are disappearing, which is real progress that a speed number will not show.
Is a faster response time a sign of improvement?
Only alongside accuracy. Speed and accuracy trade against each other, so a falling median with falling accuracy is a change of strategy rather than a gain in skill. A falling median with steady accuracy at the same mode and difficulty is the pattern worth taking seriously.

Sources

  1. To transform or not to transform: using generalized linear mixed models to analyse reaction time data (opens in a new tab)Frontiers in Psychology — accessed
  2. Housing Purchase Affordability, UK: 2024 (glossary: median) (opens in a new tab)Office for National Statistics — accessed
  3. The speed-accuracy tradeoff: history, physiology, methodology, and behavior (opens in a new tab)Frontiers in Neuroscience — accessed

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