Normal and Skewed Distributions in Psychology: A-Level Guide

When Theodore Micceri tested 440 large sets of psychology and education scores for a normal distribution, every single one failed the test (Micceri, 1989). The bell curve is the model, but real data are often skewed.

Draw a graph of almost any set of scores from a psychology study and a shape appears. Sometimes it is the neat, symmetrical bell curve that fills textbooks. More often it leans to one side, with scores bunched up at one end and a long, thin tail trailing off at the other. That shape is not decoration. It tells you which average to trust, which statistical test you can use, and sometimes that something went wrong with the study itself.

For A-level Psychology, the AQA specification asks you to know “the characteristics of normal and skewed distributions” and gives a typical exam task: being handed a set of scores and asked to mark where the mean, median or mode would fall (AQA, 2021). To do that well you need to be comfortable with averages and with spread, so if standard deviation is still a bit hazy, it is worth a quick look first.

This guide works through the questions students ask in the order they usually ask them: what a normal distribution is, what makes a distribution skewed, where the averages sit on each shape, what causes skew in the first place, and why any of this matters when you choose a statistical test. There is an interactive explorer part-way through, so you can drag a curve into shape and paste in your own data to see which way it leans.

What Is a Normal Distribution in Psychology?

A normal distribution in psychology is a pattern of scores that forms a symmetrical, bell-shaped curve when it is plotted on a graph. Most people score close to the average, fewer people score a little above or below it, and only a handful score at the extremes. Because of its shape it is often called the bell curve, and it is also known as the Gaussian distribution after the mathematician Carl Friedrich Gauss.

Picture a frequency graph. The scores run along the horizontal axis, from low on the left to high on the right, and the height of the curve shows how many people got each score. In a normal distribution the highest point is exactly in the middle, and the curve slopes away evenly on both sides. If you folded the graph down the centre line, the two halves would match.

The normal distribution is really a mathematical model rather than something you see perfectly in a real sample. A real set of scores is lumpy, especially a small one. When psychologists say data are “normally distributed” they mean the scores are close enough to that ideal shape for the model to be useful.

The Characteristics of a Normal Distribution

The characteristics of a normal distribution are the features examiners expect you to list and recognise. There are five that matter at A-level:

1. It is symmetrical. The left half of the curve is a mirror image of the right half.
2. The mean, median and mode are equal. All three averages fall at the same point, the peak in the centre of the curve.
3. Most scores cluster around the middle. The curve is highest at the centre and scores become steadily less common the further you move from it.
4. The tails never touch the horizontal axis. In the mathematical model the two tails get closer and closer to zero without ever reaching it. This is described as asymptotic, and it means extreme scores are very rare but never strictly impossible.
5. It has a fixed relationship with the standard deviation. A known proportion of scores always falls within one, two and three standard deviations of the mean, whatever the variable being measured.

The 68-95-99.7 Rule

The 68-95-99.7 rule says that in a normal distribution about 68% of scores fall within one standard deviation of the mean, about 95% within two, and about 99.7% within three. The precise figures from the US National Institute of Standards and Technology are 68.27%, 95.45% and 99.73% (NIST/SEMATECH, n.d.-b). The rule is sometimes called the empirical rule.

Because the curve is symmetrical, the share outside is split equally between the two tails. So about 2.3% of scores fall more than two standard deviations below the mean, and another 2.3% fall more than two above it. This is the logic behind converting a raw score into a z-score, which simply tells you how many standard deviations a score sits from the mean.

Normal Distribution Examples in Psychology

The best-known example of a normal distribution in psychology is IQ. Intelligence tests are built and scored so that results in the population form a bell curve with a mean of 100. A score below 70 is described as two standard deviations below that mean, which puts the standard deviation at 15 points (National Academies of Sciences, Engineering, and Medicine, 2015).

Put those numbers through the 68-95-99.7 rule and the curve comes to life. About 68% of people score between 85 and 115, about 95% between 70 and 130, and about 99.7% between 55 and 145. Only around 2.3% score below 70. That last figure matters, because the statistical infrequency definition of abnormality treats scores that far from the mean as unusual, as the article on defining abnormality explains. Take care not to read too much into it: IQ is normal because the tests are designed to produce that shape, not because nature guarantees it.

Other variables that psychologists often treat as roughly normal include scores on well-designed personality questionnaires and performance on tests that are pitched at the right level of difficulty for the people taking them. Physical measures such as adult height are the classic non-psychology example. In each case the data only look normal when the sample is large and the measure has room for scores to spread out in both directions.

Why So Many Things Follow a Bell Curve

Many things follow a bell curve because they are the combined result of lots of small, independent influences. Think about memory span. It is shaped by genes, sleep, practice, motivation on the day, how familiar the material is, background noise and dozens of other factors. For most people these pushes and pulls roughly cancel out, leaving them near the middle. Only a few people get almost every factor working for them, or almost every factor working against them, which is why the extremes are rare.

Karl Pearson, one of the founders of modern statistics, described the usual derivation of the normal curve in exactly these terms: a very large number of small “contributory causes”, each equally likely to push a score up or down. He then showed that when those conditions are not met, the result is an asymmetrical curve, which he called skew variation (Pearson, 1895).

What Is a Skewed Distribution?

A skewed distribution is a distribution of scores that is not symmetrical. Most of the scores pile up towards one end of the scale, and a long, thin tail stretches out towards the other. The direction of the skew is named after the tail, not the pile of scores, which is the single most common thing students get the wrong way round.

Pearson (1895) identified two quite different reasons a curve can be lopsided. The first is a mixed sample: two different groups measured together can produce an uneven shape. The second is a genuine imbalance, where scores simply have more room, or more reason, to stray in one direction than the other. Both still turn up in psychology research more than a century later.

Positive Skew (Skewed to the Right)

A positive skew is a distribution in which most scores are low and a long tail stretches out to the right, towards the high scores. It is also called right skew. The peak of the curve sits to the left of centre, and a small number of unusually high scores trail off into the tail.

A test that is too difficult for the people taking it is the classic example. If a memory test asks participants to recall 40 unrelated words after a single hearing, most people will recall only a few, a handful will do quite well, and one or two exceptional scorers will stretch the tail out to the right. The scores cannot go below zero, so they bunch up against that lower limit.

Income is the textbook real-world example. The UK median household disposable income in the financial year ending 2024 was £36,700 (Office for National Statistics [ONS], 2025). The ONS cautions that the mean can be heavily influenced by a small number of people with very high incomes, which is exactly what a positive skew looks like: a few very large values stretching the tail and dragging the mean upwards.

Negative Skew (Skewed to the Left)

A negative skew is a distribution in which most scores are high and a long tail stretches out to the left, towards the low scores. It is also called left skew. The peak sits to the right of centre, and a small number of unusually low scores trail off to the left.

A test that is too easy produces a negative skew. If a class of sixth-formers sits a spelling test pitched at primary-school level, most will score 18, 19 or 20 out of 20. A few who were distracted or unwell will score lower, and they form the tail. Nobody can score above the maximum, so the scores pile up against that upper limit.

Positive vs Negative Skew Compared

Positive and negative skew are mirror images of each other, so the quickest way to learn them is side by side.

Where Are the Mean, Median and Mode in a Skewed Distribution?

In a skewed distribution the mode sits at the peak, the median sits a little towards the tail, and the mean sits furthest towards the tail. In a positive skew that gives the order mode, then median, then mean from lowest to highest. In a negative skew the order flips: mean, then median, then mode. In a normal distribution all three are in the same place.

Why the Mean Moves Towards the Tail

The mean moves towards the tail because it is the only one of the three averages that uses the actual size of every score. The mode only cares which score is most common, so it stays at the peak. The median only cares about the middle position once the scores are in order, so a very high score counts no more than a slightly high one. The mean adds every score together, so one extreme value can shift it a long way.

Imagine five friends earning £20,000, £22,000, £24,000, £26,000 and £28,000. The mean and median are both £24,000. Now replace the top earner with someone on £278,000. The median does not move, because the middle person still earns £24,000. The mean jumps to £74,000, a figure that describes nobody in the group. That is positive skew in miniature, and it is why the ONS prefers the median for the income of a “typical” person (ONS, 2025).

How to Remember the Order

The simplest way to remember the order is that the mean follows the tail. Find the tail, and the mean is the average nearest to it. The mode is always at the top of the hump, and the median is always between the two.

A second trick uses the alphabet. Mean, median and mode are in alphabetical order, and that is their order from left to right in a negative skew, where the tail is on the left. Reverse the alphabet for a positive skew: mode, median, mean. If you remember only one, remember “the mean follows the tail”, because it also works when you are handed a set of numbers rather than a picture.

Worked Example: A Positively Skewed Set of Scores

A researcher counts how many errors 11 participants make on a difficult proofreading task. The scores, in order, are 0, 1, 1, 1, 2, 2, 3, 4, 6, 9 and 15.

1. Mode. The score that appears most often is 1 (three times), so the mode is 1.
2. Median. With 11 scores the middle one is the 6th, which is 2, so the median is 2.
3. Mean. The scores add up to 44, and 44 divided by 11 is 4, so the mean is 4.
4. Order. Mode (1), then median (2), then mean (4). The mean is highest, so the data are positively skewed. The scores of 9 and 15 form the tail and drag the mean upwards.

Worked Example: A Negatively Skewed Set of Scores

A teacher gives 11 students an easy test marked out of 20. The scores, in order, are 8, 14, 16, 17, 18, 18, 19, 19, 19, 20 and 20.

1. Mode. 19 appears three times, more than any other score, so the mode is 19.
2. Median. The 6th score is 18, so the median is 18.
3. Mean. The scores add up to 188, and 188 divided by 11 is 17.09 to two decimal places.
4. Order. Mean (17.09), then median (18), then mode (19). The mean is lowest, so the data are negatively skewed. The score of 8 is the tail pulling the mean down.

Exam questions often go the other way and give you only the three averages. If the mean is 12, the median 10 and the mode 9, the mean is highest, so the distribution is positively skewed. If the mean is 42, the median 45 and the mode 47, the mean is lowest, so the distribution is negatively skewed.

When the Textbook Rule Breaks

The textbook rule that the mean sits on the tail side of the median is a strong rule of thumb, not a law. Paul von Hippel (2005) showed that it “fails with surprising frequency” in real data. It can break when a distribution has more than one peak, when one tail is long but the other is heavy, and most often when the scores can only take a few whole-number values, so the areas either side of the median are not equal.

For the A-level exam, use the standard rule: examiners expect it, and it works for the smooth, single-peaked curves they draw. It is still worth knowing the limits, because a strong evaluation answer can point out that small samples of whole-number scores do not always behave as neatly as the diagram suggests.

Skewed Distribution Calculator and Explorer

The explorer below lets you drag a curve from negative skew through normal to positive skew and watch the mean, median and mode separate. Underneath it, paste in any set of scores and it will calculate the three averages, the standard deviation and a skewness value, then tell you which way the data lean. The two worked examples above are loaded as presets so you can check the answers.

The skewness figure the calculator reports is the adjusted Fisher-Pearson coefficient, the version most statistics software uses (NIST/SEMATECH, n.d.-a). A positive value means positive skew and a negative value means negative skew. The calculator labels anything between -0.5 and +0.5 as roughly symmetrical, which is a practical cut-off for a teaching tool rather than an official standard.

What Causes a Skewed Distribution?

A skewed distribution is usually caused by a limit that stops scores spreading out equally in both directions. When scores hit a floor or a ceiling they bunch up against it, and the only direction left for them to spread is away from the limit, which creates the tail. Outliers, mixed samples and small samples can also produce skew.

Floor Effects and Positive Skew

A floor effect happens when a task is so hard that most participants score at or near the lowest possible score. Because no one can score below zero, the scores pile up at the bottom and a few stronger performers form a tail to the right. The result is a positive skew.

Floor effects are more than a quirk of the graph. They are a problem for the study's conclusions. If a memory experiment compares two revision techniques but the test is so hard that both groups score close to zero, there is no room left for a difference to show. The researcher might wrongly conclude the techniques are equally effective when the test simply could not detect the difference. That makes a floor effect a threat to the validity of the measure, and the fix is to pilot the task and adjust its difficulty before the real study begins.

Ceiling Effects and Negative Skew

A ceiling effect is the opposite: a task so easy that most participants score at or near the maximum. The scores pile up against the top of the scale, a few weaker performances form a tail to the left, and the result is a negative skew.

Ceiling effects cause the same problem in reverse. If both conditions of an experiment score close to full marks, any real difference between them is hidden. Satisfaction ratings and wellbeing questionnaires can show the same pattern when most people tick the top box, which leaves the researcher unable to tell the fairly satisfied from the delighted.

Natural Limits: Reaction Times

Reaction times are a classic example of positively skewed data in cognitive psychology. Lo and Andrews (2015) note that the distribution of reaction times in simple decision tasks is "invariably positively skewed". There is a physical limit on how fast anyone can respond, so fast responses bunch up just above that limit. Slow responses, caused by a lapse of attention, a moment of doubt or a sneeze, have no upper limit at all, so they stretch out a long tail to the right.

This has practical consequences. Researchers working with reaction times cannot simply assume their data are normal, and they have to decide whether to transform the scores, use the median, or choose an analysis built for skewed data. Lo and Andrews (2015) argue that transforming reaction times to force them into a normal shape can change the conclusions a study reaches, so the choice is not a trivial one.

Outliers, Mixed Samples and Small Samples

Outliers, mixed samples and small samples can all make data look skewed even when the underlying variable is not. A single participant who misunderstood the instructions can stretch a tail on their own. A sample that mixes two different groups, such as children and adults on the same reading test, can produce a lopsided or double-peaked shape, which is the heterogeneous-material cause Pearson (1895) described. A sample of ten people is lumpy almost by definition, so an apparent skew may just be chance.

This is why the way participants are chosen matters. A biased or very small sample, covered in the guide to sampling methods in psychology, can create a skew that says more about who was recruited than about the behaviour being studied.

Skewed Distribution Examples in Psychology

Skewed distributions turn up across psychology whenever a measure has a natural limit at one end. The table below gives examples of the kind exam questions describe, with the reason for the skew in each case.

The same variable can change shape depending on who is measured. A reading test that is normally distributed for ten-year-olds will be negatively skewed for adults, who mostly reach the ceiling, and positively skewed for five-year-olds, who mostly sit near the floor. That is a useful point to make in an evaluation answer: the distribution describes a particular sample on a particular measure, not a fixed property of the behaviour.

Why the Shape of a Distribution Matters for Statistical Tests

The shape of a distribution matters because parametric statistical tests, such as the t-test and Pearson's r, assume the data come from a normally distributed population. If the data are badly skewed, a non-parametric test that works with ranks, such as the Mann-Whitney U test or the Wilcoxon signed-rank test, is usually the safer choice.

Parametric tests use the mean and standard deviation in their calculations. Both are pulled around by a long tail, so a skewed sample can make those tests less trustworthy. Blanca and colleagues (2013) put it simply: parametric statistics "are based on the assumption of normality". Non-parametric tests turn scores into ranks first, so an extreme score becomes just the highest rank rather than a huge number, and the tail loses its power to distort the result.

The full decision process is set out in the guide on which statistical test to use, and each test has its own worked example: the t-test, the Mann-Whitney U test, the Wilcoxon signed-rank test and Spearman's rho. Normality sits alongside the level of measurement as one of the two questions that decide between them.

How Normal Is Real Psychology Data?

Real psychology data are normal far less often than textbooks imply. Micceri (1989) examined 440 large-sample achievement and psychometric measures and found every one of them significantly non-normal. Among the problems he recorded were lopsided distributions, several peaks where there should have been one, and modes that fell outside the range between the mean and the median.

Small samples fare no better. Blanca and colleagues (2013) analysed 693 real distributions of between 10 and 30 scores, covering cognitive ability and other psychological variables. Taking skewness and kurtosis together, only 5.5% were close to what a normal distribution would produce, although truly extreme departures were not common. Their conclusion was that normality "is not the rule" with real data.

None of this means parametric tests are useless. Micceri himself cautioned that his distributions did not match the extreme shapes used in earlier research on how badly the tests fail, and Blanca and colleagues found severe departures from normality were uncommon. What it does mean is that checking the shape of your data is a real step, not a formality, and that "the data were normally distributed" is a claim to be tested rather than assumed.

How to Tell if Data Are Normally Distributed or Skewed

You can tell whether data are normal or skewed by drawing a graph, comparing the mean with the median, or calculating a skewness statistic. At A-level the first two are all you need. The third is what researchers report in published papers.

1. Draw a histogram. Plot the scores as a histogram or frequency polygon and look at the shape. A symmetrical hump suggests normal data; a hump to one side with a long tail suggests skew. The US National Institute of Standards and Technology describes the histogram as an effective way of showing skewness (NIST/SEMATECH, n.d.-a).
2. Compare the mean and the median. If they are close, the data are roughly symmetrical. If the mean is clearly higher than the median, the data are positively skewed. If it is clearly lower, the data are negatively skewed.
3. Calculate a skewness statistic. Software reports a skewness value. Zero means perfectly symmetrical, a positive number means positive skew and a negative number means negative skew (NIST/SEMATECH, n.d.-a). The further from zero, the stronger the skew.

A simple version of the skewness statistic makes the link with the averages explicit. Pearson's second skewness coefficient is three times the mean minus the median, divided by the standard deviation (NIST/SEMATECH, n.d.-a). When the mean is above the median the answer is positive, and when it is below the answer is negative, exactly as the "mean follows the tail" rule predicts. For the proofreading example above, that gives 3 × (4 − 2) ÷ 4.49, which is about 1.34, a clear positive skew.

What About Kurtosis?

Kurtosis describes how heavy the tails of a distribution are compared with a normal curve. A distribution with high kurtosis has more extreme scores, or outliers, than a normal distribution would, while one with low kurtosis has fewer (NIST/SEMATECH, n.d.-a). Kurtosis is not on the AQA specification, but it is the second number researchers check alongside skewness, and it is the other half of the Blanca et al. (2013) findings described above.

The Normal Distribution, Standard Deviation and Z-Scores

The normal distribution, the standard deviation and z-scores work together as one system. The standard deviation measures how spread out the scores are, the normal curve says what proportion of people fall within each band of standard deviations, and a z-score locates any individual score on that curve.

Take an IQ of 130. It sits two standard deviations above the mean of 100, so its z-score is +2. From the 68-95-99.7 rule, about 95.45% of people fall within two standard deviations either side, which leaves roughly 2.3% above 130. A person scoring 130 has therefore scored higher than about 97.7% of the population. That chain of reasoning only works if the scores really are normally distributed. On a skewed measure the same z-score would point to a different percentage, which is one more reason to check the shape first.

The standard deviation of individual scores should not be confused with the standard error, which describes how much a sample mean would vary from sample to sample. The two are related, but they answer different questions.

Normal and Skewed Distributions in the A-Level Exam

In the AQA A-level Psychology exam, normal and skewed distributions appear under data handling and analysis, alongside measures of central tendency and dispersion (AQA, 2021). Questions are usually short and worth a few marks, but they come up often because they test whether you understand the averages rather than just calculate them.

Common Question Types

• Identify the distribution. You are given a graph, or the mean, median and mode, and asked whether it is normal, positively skewed or negatively skewed.
• Mark the averages. You are given a sketch of a skewed curve and asked to label where the mean, median and mode would be.
• Explain the skew. You are told about a study, such as a test that was too easy, and asked to explain why the results are skewed.
• Choose an average. You are asked which measure of central tendency is most appropriate for skewed data, and why. The answer is usually the median, because extreme scores do not distort it.
• Link to testing. You are asked why skewed data might lead a researcher to choose a non-parametric test.

Common Mistakes to Avoid

• Naming the skew after the hump. The skew is named after the tail. A hump on the left with a tail on the right is a positive skew.
• Putting the mean at the peak. The peak of any curve is the mode. The mean is only at the peak in a normal distribution.
• Swapping the median and the mode. The median is always between the other two in a skewed distribution.
• Using the mean for skewed data without comment. If the data are skewed, say why the median is the better summary.
• Saying data "are" normal because the graph looks roughly symmetrical. With a small sample it is safer to say the data "appear" roughly normal.

A strong answer to a skew question usually does three things: names the distribution correctly, justifies it from the order of the averages or the direction of the tail, and links it to the study, such as pointing to a floor or ceiling effect. That pattern of identify, justify and link works for most short data-handling questions and is part of the wider quantitative analysis skills the exam rewards.

Conclusion

A normal distribution is a symmetrical bell curve with the mean, median and mode together in the middle and a fixed share of scores within each standard deviation. A skewed distribution leans to one side, and it is named after its tail: positive when the tail points to the high scores, negative when it points to the low scores. In both cases the mean follows the tail, so the order of the three averages reveals the shape even without a graph.

Skew is usually caused by a floor, a ceiling or a natural limit, and it matters for more than exam marks. It tells you when the median is a fairer summary than the mean, warns you when a task was pitched at the wrong level, and helps decide between a parametric and a non-parametric test. Given how rarely real data turn out perfectly normal, checking the shape before analysing it is one of the most useful habits a psychology student can build.

Frequently Asked Questions

What is a normal distribution in psychology in simple terms?

In simple terms, a normal distribution means most people score around the average and fewer and fewer people score further away from it in either direction. On a graph this makes a symmetrical bell shape. IQ is the standard psychology example, with a mean of 100 and most people scoring between 85 and 115.

What is a skewed distribution in psychology?

A skewed distribution in psychology is a set of scores that is lopsided rather than symmetrical, with most results bunched at one end and a long tail at the other. It often happens when a task is too hard or too easy for the participants, so their scores pile up against the lowest or highest possible mark.

What is the difference between positive skew and negative skew?

Where are the mean, median and mode in a negatively skewed distribution?

In a negatively skewed distribution the mean is lowest, the median is in the middle and the mode is highest. The mode sits at the peak on the right, and the few very low scores in the left-hand tail pull the mean down below the median.

What causes a positively skewed distribution?

A positively skewed distribution is usually caused by a lower limit that scores cannot go below, such as zero errors, zero words recalled or the fastest humanly possible reaction time. Scores bunch against that floor, and a few high scores stretch a tail to the right. A task that is too difficult is the typical cause in an experiment.

What are some examples of skewed distributions in real life?

Household income is positively skewed, because a small number of very high earners pull the mean above the median. Reaction times are positively skewed too. Marks on a test that almost everyone finds easy are negatively skewed, as are ratings where most people pick the top option on the scale.

What is the 68-95-99 rule?

The 68-95-99 rule, more fully the 68-95-99.7 rule, states the share of a normal distribution that falls within one, two and three standard deviations of the mean. About 68% of scores lie within one, about 95% within two, and about 99.7% within three. It only applies to data that are normally distributed.

What is a bell curve in psychology?

A bell curve in psychology is another name for the normal distribution, the smooth, symmetrical shape that scores make when most people cluster around the middle and extreme results are rare. Psychologists use it to judge how typical a score is, for example deciding that an IQ of 130 is higher than roughly 98% of people.

References

• AQA. (2021). AS and A-level Psychology specification (7181, 7182) (Version 1.2). Assessment and Qualifications Alliance.
• Blanca, M. J., Arnau, J., López-Montiel, D., Bono, R., & Bendayan, R. (2013). Skewness and kurtosis in real data samples. Methodology, 9(2), 78–84.
• Lo, S., & Andrews, S. (2015). To transform or not to transform: Using generalized linear mixed models to analyse reaction time data. Frontiers in Psychology, 6, Article 1171.
• Micceri, T. (1989). The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin, 105(1), 156–166.
• National Academies of Sciences, Engineering, and Medicine. (2015). Mental disorders and disabilities among low-income children. The National Academies Press.
• NIST/SEMATECH. (n.d.-a). Measures of skewness and kurtosis. In e-Handbook of statistical methods. National Institute of Standards and Technology.
• NIST/SEMATECH. (n.d.-b). What do we mean by "normal" data? In e-Handbook of statistical methods. National Institute of Standards and Technology.
• Office for National Statistics. (2025). Average household income, UK: Financial year ending 2024. ONS.
• Pearson, K. (1895). Contributions to the mathematical theory of evolution. II. Skew variation in homogeneous material. Philosophical Transactions of the Royal Society of London. A, 186, 343–414.
• von Hippel, P. T. (2005). Mean, median, and skew: Correcting a textbook rule. Journal of Statistics Education, 13(2).

Further Reading and Research

Recommended Articles

• Statistical Significance: P-Values, Errors and Effect Sizes
• What Is a Correlation Coefficient? Pearson's r and Psychology Statistics
• The Sign Test: Formula, Worked Example and Critical Values

Suggested Books

• Field, A. (2024). Discovering statistics using IBM SPSS Statistics (6th ed.). SAGE.
  • The standard university text for psychology statistics, with a full chapter on checking assumptions including normality, skew and kurtosis, written in an informal, jokey style.
• Coolican, H. (2019). Research methods and statistics in psychology (7th ed.). Routledge.
  • A long-standing favourite for A-level and undergraduate students that covers distributions, descriptive statistics and choosing tests in plain language.
• Spiegelhalter, D. (2019). The art of statistics: Learning from data. Pelican.
  • A readable, non-technical tour of how statistics works in the real world, including why averages mislead when data are skewed.

Recommended Websites

• NIST/SEMATECH e-Handbook of Statistical Methods
  • A free, authoritative US government reference with clear pages on the normal distribution, skewness, kurtosis and histograms.
• AQA A-level Psychology specification
  • The official specification, including the mathematical requirements that set out exactly what you need to know about distributions.
• Office for National Statistics
  • UK official statistics, where the household income releases show a skewed distribution and the case for using the median.

Kathy Brodie

Kathy Brodie is an Early Years Professional, Trainer and Author of multiple books on Early Years Education and Child Development. She is the founder of Early Years TV and the Early Years Summit.

Kathy's Author Profile

To cite this article please use:

Early Years TV Normal and Skewed Distributions in Psychology: A-Level Guide. Available at: https://www.earlyyears.tv/normal-skewed-distributions-psychology/ (Accessed: 11 October 2026).