# Normal Distribution

## What is a Normal Distribution?

The normal distribution is a pattern for the distribution of a
set of data which follows a bell shaped curve.
• µ is the mean of the set of data.
• σ is the standard deviation of the same set of data The bell shaped curve has several properties:
• The curve concentrated in the center and decreases on either side.
This means that the data has less of a tendency to produce unusually
extreme values.
• The bell shaped curve is symmetric. This tells you that he probability
of deviations from the mean are comparable in either direction.

If a data distribution is approximately normal then
• about 68% of the values are within 1 standard deviation of the mean
(mathematically, µ ± 1σ, where µ is the arithmetic mean),
• about 95% of the values are within 2 standard deviations (µ ± 2σ), and
• about 99.7% lie within 3 standard deviations (µ ± 3σ).

## How to interpret a Normal Distribution? Population Size = 3000 pupils sat for Science Test Average score = 50 marks and SD = 5 Means that 68% or 2/3 of the 3000 pupils have scored 5 marks around the average, OR 2000 pupils scored from 45 to 55 marks. Population Size = 3000 pupils sat for Science Test Average score = 50 marks and SD = 10 Means that 68% or 2/3 of the 3000 pupils have scored 10 marks around the average, OR 2000 pupils scored from 40 to 60 marks