# Normalised Histogram

Discussion in 'Mathematics' started by pipipi, Mar 24, 2011.

1. ### pipipi

are you going to add the normal distribution curve?

2. ### bbibblerNew commenter

Both the histogram and cumulative histogram have
an additional variant whereby the counts are
replaced by the normalized counts. The names for these variants
are the relative histogram and the relative cumulative
histogram.

There are two common ways to normalize the counts.

<ol>[*]The normalized count is the count in a class divided by
the total number of observations. In this case
the relative counts are normalized to sum to one
(or 100 if a percentage scale is used).
This is the intuitive case where the height of
the histogram bar represents the proportion of the
data in each class.

[*]The normalized count is the count in the class
divided by the number of observations times the
class width. For this normalization, the area
(or integral) under the histogram is equal to one.
From a probabilistic point of view, this normalization
results in a relative histogram that is most akin to
the probability density function and a relative
cumulative histogram that is most akin to the
cumulative distribution function. If you want to
overlay a probability density or cumulative
distribution function on top of the histogram, use
this normalization. Although this normalization is
less intuitive (relative frequencies greater than 1
are quite permissible), it is the appropriate
normalization if you are using the histogram to model
a probability density function.
</ol>
GIYF

The area under the graph is equal to 1

3. ### noseygeorgeNew commenter

Nice one - thank you.