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The normal distribution
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Many human characteristics, such as height or IQ, form a typical pattern when plotted: the normal distribution.
Features
When the scores are plotted on a graph (such as a histogram), a normal distribution makes a bell-shaped curve.
It is symmetrical: the left and right halves are mirror images.
The mean, median and mode are all the same, at the centre (the highest point).
Most scores are close to the middle; fewer and fewer scores are found towards the extremes (very high or very low).
It is symmetrical: the left and right halves are mirror images.
The mean, median and mode are all the same, at the centre (the highest point).
Most scores are close to the middle; fewer and fewer scores are found towards the extremes (very high or very low).
Examples
IQ scores are designed to be normally distributed, with a mean of 100: most people score close to 100, and very few score much higher or lower.
Height, reaction times in large groups and many personality test scores are roughly normally distributed.
If a set of scores is normally distributed, the mean is a good summary because it sits at the centre.
Height, reaction times in large groups and many personality test scores are roughly normally distributed.
If a set of scores is normally distributed, the mean is a good summary because it sits at the centre.
Not normal
If data is not symmetrical, it is skewed: the tail is longer on one side, and the mean, median and mode are different.
Example: if a test is very easy, most people score highly and a few score low, so the curve is lopsided.
Recognising the shape of data helps you choose the right average: with skewed data, the median is often better.
Example: if a test is very easy, most people score highly and a few score low, so the curve is lopsided.
Recognising the shape of data helps you choose the right average: with skewed data, the median is often better.
In a normal distribution of test scores, the mean is 50. What are the median and the mode?
- In a normal distribution, the mean, median and mode are equal.
- So all three are 50.
Answer: Median = 50 and mode = 50.
A normal distribution is bell-shaped and symmetrical, with the mean, median and mode equal at the centre. Most scores cluster near the middle and few are at the extremes. IQ is a common example, with a mean of 100.
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