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Explanation of a Normal Distribution Curve

Graphs a fantastic way of allowing us to easily analyse data without having to put a great amount of into making sense of our research. You’ll notice that, when data points are assembled on a graph, it creates a striking visual look that is either distributed unevenly – more data on the right, or more data on the left, for example – or is all jumbled up, as below:

statistical data analysis schema

Sometimes, though, data is distributed evenly around a central value, which is the greatest number of value, and is consequently the highest point. To the left and the right, the data descends equally, creating a look of perfect symmetry. We call this a normal distribution curve:

A normal curve distribution, also referred to as a bell curve or Gaussian distribution, looks as striking as it does because the data is centred around a central value – or mean.

Because of this, the data is symmetrical which allows us to estimate that subsequent outcomes will lie within a certain ‘range’ to the left or right of the mean.

What Is The Mean?

The mean, which is also referred to as the central value at the heart of the normal probability curve, is the average of the results. Because most values to the left and right of the mean are within 3 standard deviations, the normal distribution curve creates the symmetrical, flowing shape that it does.

Calculating the mean is fairly easy.

Let’s say that 95% of men at your workplace are between 5’11” and 6’3” in height. The mean subsequently is the average between the two heights, with us being able to surmise that at least 95% of the guys will fall between these two heights.

Mean = (5.11 + 6.3) / 2 = 6.1

What Causes A Normal Curve Distribution?

A few things create the distinct normal distribution curve. They include:

  • Exam results
  • Peoples heights
  • Blood pressure results

Surveys into peoples’ height will often result in a normal distribution curve. Let’s say the average height of males is 6’11” in Ohio. There will subsequently be about 3 standard deviations to the left and right of this central value.

What Is A Standard Deviation?

Standard deviations are important to understand. On a normal curve distribution graph, there are usually about 3 standard deviations either side of the central value.

There is a good chance that something will be 1 standard deviation of the mean.

There is a very good chance that something will be 2 standard deviations of the mean.

It’s certain that something will fall within 3 standard deviations of the mean.

This is because about 65% of the area underneath the curve lies within the the first standard deviation – which means there is a ‘good chance’ something will fall here.

95% of the area underneath your curve lies within 2 standard deviations – which means there is a very good chance something will be here.

99.7% of the area underneath the curve lies within 3 standard deviations – meaning we are able to confidently claim that it is certain something will fall here.

This means that, if the average height of males in Ohio is 6’11”, 99.7% of males are within 3 standard deviations of this average.

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