Gr 12: THE NORMAL DISTRIBUTION – an Overview
Many observations relate to a variable that is discrete:
that means that there are only certain values that it
can take: imagine the observer starting out with a pre-
printed list of all the possible values and then recording
his observations in a tally table.
Sometime the pre-printed list would be very long
(imagine one that could be used to record the amount
of money (in cents) in shoppers’ purses). Sometimes all
we can say beforehand about the values observed is
that they will lie within a certain range, but without
being able to split that range up into useful intervals.
Then the variable we are recording is called
continuous.
Often the continuous variable that we are observing will
come from a Normal distribution. The frequency
histogram for such a situation would have many many
columns, and it makes sense to consider rather the
frequency polygon: but then once that has been fitted
onto a page, the polygon looks like a smooth curve.
This curve is the graph of the frequency distribution.
The shape of the frequency distribution for the Normal
distribution is the famous bell-shaped curve
mean mean
mean
Key features to note are:
- the mean, median and mode are all the same,
corresponding to
the highest position of the graph
- the graph has reflective symmetry
Many observations relate to a variable that is discrete:
that means that there are only certain values that it
can take: imagine the observer starting out with a pre-
printed list of all the possible values and then recording
his observations in a tally table.
Sometime the pre-printed list would be very long
(imagine one that could be used to record the amount
of money (in cents) in shoppers’ purses). Sometimes all
we can say beforehand about the values observed is
that they will lie within a certain range, but without
being able to split that range up into useful intervals.
Then the variable we are recording is called
continuous.
Often the continuous variable that we are observing will
come from a Normal distribution. The frequency
histogram for such a situation would have many many
columns, and it makes sense to consider rather the
frequency polygon: but then once that has been fitted
onto a page, the polygon looks like a smooth curve.
This curve is the graph of the frequency distribution.
The shape of the frequency distribution for the Normal
distribution is the famous bell-shaped curve
mean mean
mean
Key features to note are:
- the mean, median and mode are all the same,
corresponding to
the highest position of the graph
- the graph has reflective symmetry
