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Normal Distribution Psychology

We use distributions to create graphs 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 characteristics are normally distributed in the population, meaning most individuals will score around the average, with few people being above or below the mean.

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# Normal Distribution Psychology

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We use distributions to create graphs 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 characteristics are normally distributed in the population, meaning most individuals will score around the average, with few people being above or below the mean.

• We are going to explore normal distributions in psychological research.
• First, we will provide a normal distribution definition in the context of psychology.
• Then we will establish the features of normal distributions in psychology.
• We will discuss the bell curve in normal distributions and the significance of the mean, median, and mode in normal distributions.
• Finally, we will highlight normal and skewed distributions and how normal distributions are used in psychology.

## Normal Distribution: Psychology Definition

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. An IQ (intelligence) test is a classic example of a normal distribution in psychology.

Most people tend to have an IQ score between 85 and 115, and the scores are normally distributed. Height, shoe size or personality traits like extraversion or neuroticism tend to be normally distributed in a population.

Fig. 1 - Normal distributions are characterised by their notable bell shapes¹.

## Features of Normal Distributions in Psychology

Normal distributions have distinct features. They are symmetrical, meaning that the distribution of scores larger than the mean should be symmetrical to the distribution of scores smaller than the mean. Normally distributed data forms a bell curve. The mean, median and mode values are similar or the same, creating the distribution's centre (the peak).

The distribution's tails meet the x-axis at infinity, meaning they shouldn't touch the x-axis (asymptotic). An equal amount of extreme scores should fall on both sides of the mean.

## Normal Distribution Bell Curve in Psychology

The normal distribution can be illustrated with a bell curve in that it's shaped like a bell, which suggests that most of our data is clustered around the mean value in the distribution centre. The probability of values being close to the mean is much higher than those far from the mean because the frequency of scores at the distribution's tails is much lower than in the centre.

## The Mean, Median, and Mode in a Normal Distribution

When the data is normally distributed, the mean, median, and mode tend to be the same or similar. Let's recap what each value indicates and how to calculate them.

• The mean is the average value of our data. To calculate the mean, add all the values collected and divide their sum by the number of data points (e.g. the number of participants or measurements).
• The median is the middle value in your data set. Order your data from the lowest to the highest value to find the median. If your number of data points is odd (e.g. 7), choose the value in the middle (the fourth value); if it's even (e.g. 8), then your median is the average of the two middle values (the average of the fourth and the fifth value).
• The mode is the most frequently repeating value in your data set. To find the mode, order your data from the lowest to the highest; the number appearing most frequently is your mode. If none of your values repeats, your data set has no mode.

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 and Skewed Distributions in Psychology

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 Distribution

Skewed distributions are not symmetrical; they have their peak off-centre and extended tails 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.

### Examples of Normal and Skewed distributions

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

Fig. 2 - A normal distribution.

The distribution won't be normal if there is a bigger difference between the mean, median and mode. Here, the mode and median are higher than the mean, suggesting that negatively skewed our data.

 Mean Median Mode 14.5 16 18

Fig. 3 - A negatively skewed distribution.

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

Fig. 4 - A positively skewed distribution.

## Normal Distribution in Psychological Testing

A normal distribution is quite important in psychological research, especially when making predictions. Here are some examples of normal distributions in psychological testing.

### Clinical Practice

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.

### Research

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. We will need to use less sensitive, nonparametric statistical tests if our data is not normally distributed.

## Normal Distribution Psychology - Key takeaways

• 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 curve, with few extreme scores. Tails of the normal distribution meet the x-axis at infinity, meaning they should be above the x-axis when graphically represented (asymptotic).
• Mean is the average value, the median is the middle value, and mode is the most frequent value in a data set. We can estimate the data distribution based on the mean, median and mode values.
• Skewed distributions are not symmetrical; they have their peak off-centre and have an extended tail in one direction.
• Normal distributions can be helpful for clinical diagnosis. In research, normally distributed data is also necessary to test the statistical significance of our results using parametric statistical tests like the t-test.

## References

1. Fig. 1: Normal Distribution by D Wells, CC BY-SA 4.0 https://creativecommons.org/licenses/by-sa/4.0, via Wikimedia Commons

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.

## Normal Distribution Psychology Quiz - Teste dein Wissen

Question

What do distributions represent?

Distributions represent how the frequency of scores is distributed.

Show question

Question

What is a normal distribution?

Normal distributions are bell-shaped and symmetrical. The mean, median and mode values are the centre of the bell, with few extreme scores.

Show question

Question

What individual characteristics are normally distributed in the population?

For example, IQ, personality traits, shoe size, height, and weight.

Show question

Question

What are the 3 main features of normal distributions?

1. They are symmetrical, meaning that the distribution of scores larger than the mean should be symmetrical to the distribution of scores smaller than the mean.

2. Normal distribution is because it is bell-shaped. The mean, median and mode values tend to be similar or the same and create the centre of the distribution.

3. The tails of the distribution meet the x-axis at infinity.

Show question

Question

How are the scores distributed in normally distributed data?

• Most of the data is clustered around the mean value that is in the centre of the distribution.
• The frequency of scores at the tails of the distribution is much lower than in the centre.
• Scores are distributed symmetrically around the mean.

Show question

Question

Let's say that anxiety is a normally distributed trait in the population. What's the probability of having average levels of anxiety compared to extreme levels of anxiety?

The probability of scoring around the average is larger than getting extreme scores in the case of normally distributed traits. This is because normal distribution suggests that anxiety levels for most people in the population will be clustered around the mean.

Show question

Question

Which value measures the average score?

mean

Show question

Question

Which value reflects the middle score?

median

Show question

Question

Which value reflects the most frequent score?

mode

Show question

Question

Is the following statement true or false?

When the data is normally distributed mean, median and mode tend to be the same or very similar.

True

Show question

Question

Which distributions are symmetrical?

Normal distributions

Show question

Question

Describe the characteristics of skewed distributions.

Skewed distributions are not symmetrical, they have their peak off centre and have an extended tail in one direction. 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.

Show question

Question

What are positively skewed distributions?

Positively skewed distributions have their peak shifted to the left with a longer tail to the right.

Show question

Question

What are negatively skewed distributions?

Negatively skewed distributions have their peak shifted to the right with a longer tail to the left.

Show question

Question

What are the applications of normal distributions in psychology?

Normal distributions can be helpful for clinical diagnosis

In research normally distributed data is also necessary to test the statistical significance of our results using parametric statistical tests like the t-test.

Show question

## Test your knowledge with multiple choice flashcards

Which value measures the average score?

Which value reflects the middle score?

Which value reflects the most frequent score?

Flashcards in Normal Distribution Psychology15

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What do distributions represent?

Distributions represent how the frequency of scores is distributed.

What is a normal distribution?

Normal distributions are bell-shaped and symmetrical. The mean, median and mode values are the centre of the bell, with few extreme scores.

What individual characteristics are normally distributed in the population?

For example, IQ, personality traits, shoe size, height, and weight.

What are the 3 main features of normal distributions?

1. They are symmetrical, meaning that the distribution of scores larger than the mean should be symmetrical to the distribution of scores smaller than the mean.

2. Normal distribution is because it is bell-shaped. The mean, median and mode values tend to be similar or the same and create the centre of the distribution.

3. The tails of the distribution meet the x-axis at infinity.

How are the scores distributed in normally distributed data?

• Most of the data is clustered around the mean value that is in the centre of the distribution.
• The frequency of scores at the tails of the distribution is much lower than in the centre.
• Scores are distributed symmetrically around the mean.

Let's say that anxiety is a normally distributed trait in the population. What's the probability of having average levels of anxiety compared to extreme levels of anxiety?

The probability of scoring around the average is larger than getting extreme scores in the case of normally distributed traits. This is because normal distribution suggests that anxiety levels for most people in the population will be clustered around the mean.

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