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We use distributions to create graphical illustrations of the frequency of different scores in a data set. Normal distributions are bell-shaped and symmetrical. The mean, median and mode values are the centre of the bell, with few extreme scores. Many individual characteristics are normally distributed in the population, meaning most individuals will score around the average, with few people being much above or below the mean.
The most popular normal distribution in psychology is the population's distribution of intelligence (IQ). People's scores on IQ tests tend to be normally distributed. Most people score around average, with rare cases of people scoring very high or very low on IQ tests. Similarly, height, shoe size or personality traits like extraversion or neuroticism tend to be normally distributed in a population.
Normal distribution of data, flaticon.com
We can define normal distributions in psychology as:
Normal distributions are bell-shaped, symmetrical graphical illustrations where values such as the mean, median and mode sit at the centre of the bell, and extreme scores tail off at either end.
Normal distributions have three main features:
The normal distribution can be illustrated with a bell curve, which suggests that most of our data is clustered around the mean value in the distribution's centre. The probability of values being close to the mean is much higher than the values being far from the mean because the frequency of scores at the distribution's tails is much lower than in the centre.
When the data is normally distributed, mean, median, and mode tend to be the same or very similar. Let's recap what each of these values indicates and how to calculate them.
You asked five students about how many hours (h) they slept last night. You collected the following data: 9h, 4h, 6h, 6h, 5h. The mean of your data is 6, the median is the middle value when the data is ordered from lowest to highest, which in our case is also 6, and the mode, which is the most frequent value, is also 6.
Normal distributions take the shape of a bell curve, flaticon.com
One of the main features of the normal distribution is symmetry and characteristic bell shape. What happens if our mean, median and mode are different and the distribution isn't symmetrical? In this case, we can identify negatively or positively skewed distribution.
Skewed distributions are not symmetrical; they have their peak off centre and extended tail in one direction. In the case of skewed distributions, the mean is no longer in the centre. It is shifted due to a large number of extreme scores to one side of the distribution. Such distributions no longer form a bell curve.
Positively skewed distributions have their peak shifted to the left with a longer tail to the right.
Negatively skewed distributions have their peak shifted to the right with a longer tail to the left.
If we know that our mean, median and mode are the same or similar, we can estimate that the data is normally distributed around these values.
| Mean | Median | Mode |
| 16 | 16.5 | 16 |
Normal distribution, StudySmarter Originals, Alicja Blaszkiewicz
If there is a bigger difference between the mean, median and mode, the distribution won't be normal. Here, the mode and median are higher than the mean, suggesting negatively skewed our data.
| Mean | Median | Mode |
| 14.5 | 16 | 18 |
In this case, our measures of central tendency are quite different; the mode and the median are lower than the mean, suggesting a positively skewed distribution.
| Mean | Median | Mode |
| 18 | 15.5 | 14 |
Normal distribution are quite important in psychological research, especially when making predictions. Here are some examples of normal distributions in psychological testing.
The normal distribution is often used in psychological testing when interpreting test scores. As many psychological traits or symptoms are normally distributed across the population, by looking at where an individual score falls on the distribution, we can get an idea of how much it deviates from the average, which can aid diagnosis or help identify people at risk.
Normal distributions are also crucial for research and statistical testing. Inferential statistical tests (e.g. the t-test) that we use to decide whether to reject our null hypothesis mostly require the data to be normally distributed. If our data is not normally distributed, we will need to use less sensitive, nonparametric statistical tests.
Normal distribution tells us about the frequency of scores. Most scores will cluster in the middle around the distribution centre, and extreme scores that are further away from the mean will be less frequent and symmetrically distributed.
Parametric statistical tests require the data to be normally distributed. We can choose an appropriate statistical test based on whether our data is normally distributed or not. So, normal distributions are important in research in psychology.
A normal distribution curve is achieved when the mean, median and mode values are similar and at the distribution centre. The normal distribution also requires symmetry and very few extreme values.
The normal distribution is bell-shaped; the mean, median and mode values are similar and at the distribution centre. The normal distribution is symmetrical and has few extreme values. The tail ends of the normal distribution are asymptotic.
We use distributions to create graphical illustrations of how the frequency of data is distributed. Normal distributions are bell-shaped and symmetrical. The mean, median and mode values are the centre of the bell, with few extreme scores.
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