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

What is a Normal Distribution

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.

 Normal Distribution 1


 

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?

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

 

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Updated: August 17, 2015 — 7:20 am
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