- 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.

## 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 |

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 |

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 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

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

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##### Frequently Asked Questions about Normal Distribution Psychology

What is the meaning of normal distribution?

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.

Why is the normal distribution so important in psychology?

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.

How to achieve a normal distribution curve 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.

What are the properties of the normal distribution in psychology?

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.

What is a normal distribution curve in psychology?

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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