Data Handling: Normal Distributions

A Normal Distribution is a type of statistical graph that takes the shape of a bell curve.
This curve is characterised by its symmetrical shape, indicating that the data is evenly distributed around the mean (the average value).
The highest point of the Normal Distribution represents the mean, median, and mode - all three measures of central tendency are the same in a perfect Normal Distribution.
Most values cluster around the centre, meaning the data values near the mean are more likely to occur.
The standard deviation is a measure of how spread out the numbers in the data set are. It determines the width of the Normal Distribution. A smaller standard deviation indicates that data values are close to the mean while a larger standard deviation shows that values are spread out over a wider range.
Within a Normal Distribution: about 68% of values fall within one standard deviation of the mean; approximately 95% of values fall within two standard deviations of the mean; and nearly 99.7% of data falls within three standard deviations of the mean.
The area under the curve represents the total number of cases (100%) and it is divided into sections known as percentiles that can be used to compare individual scores to the group.
Z-scores are a measurement of how many standard deviations a data point is away from the mean in a Normal Distribution.
Graphical representations of Normal Distributions are important in psychology to understand and analyse the behaviours and cognitive functions across a population. They can provide insights into what is considered ‘typical’ or ‘normal’.
Potential limitations of using Normal Distributions include: not all data sets follow a Normal Distribution, it assumes data is symmetrical and continuous which may not always be the case, and it may not accurately reflect real-world situations where there are extremes or outliers.