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Normal Distribution Graph and Its Meaning

What Is A Normal Distribution Graph?

When we analyse data, it is easy to analyse it on a graph. When data is presented on a graph, the way it is distributed can either by uneven – for example, more data on the left or more data on the right – or it can be all mixed up.

statistical data analysis schema

Or it can be evenly spread so that it looks pretty much symmetrical. We call this a normal distribution graph – or a bell curve. In comparison to a graph that is slanted to one side, a normal distribution chart looks pretty:


A normal distribution graph looks the way it does because the data is centred around – you guessed it – a central value, which is also referred to as the mean.

When data is not centred around a central value, it means that it has a bias – either a left or a right bias.

But What Is That Central Value?

The central value is the mean, which is the average of the numbers. Because most values – say, 95% – are within a maximum of, say, 3 standard deviations of the mean, the graph normal distribution creates a shape that looks like a bell curve:

To calculate the mean, let’s look at an example.

Let’s say that 95% of boys at school are between 5.11” and 6.3” in height. The mean – or the central value – lies halfway between the two heights.

Mean = (5.11 + 6.3) / 2 = 6.1

What Phenomena Lead To A Graph Of Normal Distribution?

A few things follow a normal distribution chart, leading to that have almost perfect symmetry. They could be:

•       Blood pressure

•        Heights of people

•        Exam marks

Our height as humans is often distributed normally, leading to a graph of normal distribution. There is an average height (mean/central value) – say 5’11” – and about 3 subsequent standard deviations left and right.

Standard Deviations

Standard deviations are useful because they tell us a few probabilities.

It’s probable that something will be 1 standard deviation of the mean.

It’s very probable that something will be 2 standard deviations of the mean.

It’s certainly probable that something will be within 3 standard deviations of the mean.

About 65% of an area underneath the curve falls within 1 standard deviation of the mean.

95% falls within 2 standard deviations, whilst 99.7% falls within 3 standard deviations of the mean on a normal distribution graph.

This means that if the mean height is 5’11”, 99.7% of us are 3 standard deviations from this central value.

If you wish to discover the probability of a normal random variable, you can use a normal distribution chart. You could use it to find out how many standard deviations from the mean the population is when it comes to height, intelligence, or even in terms of their blood pressure. As mentioned earlier, a normal distribution graph is an excellent way of determining how far from the mean exams taken by students are.

Find the normal distribution graph here today!