Plotting Normalized Curve over histogram

[Roger101]

I have a series of data (x,y) as below. I want to use this data to
create a bell curve (normal distribution) with perl. How can I do
this?
x y
1 2
2 50
3 40
4 300
5 70
6 80
7 8
8 10
9 25
10 60
11 350
12 80
13 40
14 5

By normalized curve i mean something like on the link below. Didnt know how to draw a graph here.

Really appreciate any help clues.

http://training.ce.washington.edu/WSDOT/Modules/08_specifications_qa/normal_distribution.htm

[d5e5]

Sorry, this question is way over my head. I got as far as plotting your data but it doesn't look like a bell curve... more like twin peaks. In case it helps as an example of a line graph, here's the script:

#!/usr/bin/perl
#bell_curve_line.pl
use strict;
use warnings;

use GD::Graph::lines;
my $perlscriptsdir = '/home/david/Programming/Perl';

#For some reason, installing GD::Graph didn't put save.pl in my @INC path
require "/usr/share/doc/libgd-graph-perl/examples/samples/save.pl";
my $chart_file_out = 'bell_line';
print STDERR "Processing $chart_file_out\n";

#The @data array is an array of array references
# to an array of x values and an array of y values.

my @data = (
[ qw(1 2 3 4 5 6 7 8 9 10 11 12 13 14 ) ],
[ qw(2 50 40 300 70 80 8 10 25 60 350 80 40 5 )],);

my $my_graph = new GD::Graph::lines();

$my_graph->set(
x_label => 'X',
y_label => 'Frequency?',
title => 'Frequency of Various Values of X',
y_max_value => 350,
y_min_value => 2,
y_tick_number => 10,
y_label_skip => 2,
box_axis => 0,
line_width => 3,

transparent => 0,
);

$my_graph->plot(\@data);
save_chart($my_graph, "$perlscriptsdir/data/$chart_file_out");

Running this creates a file called "bell_line.gif" (see attached).

[Roger101]

Hi David,
Thanks for your promt response.

but this a line curve of actual values.
Plot the data in a bars. Then create a curve over the bar chart. So that gives you 2 bell shaped curve. The curve will be through the center of each bar. Does it make sense?

See this link
http://training.ce.washington.edu/WSDOT/Modules/08_specifications_qa/normal_distribution.htm

Any help is greatly appreciated.

[d5e5]

I'm afraid it doesn't make much sense to me, maybe because I've forgotten the very little I learned about statistics over 35 years ago.

Here's what I don't understand: If you create a bar chart of actual data and draw a line through the centre of the top of each bar, I don't see how that makes two bell curves. Wouldn't you end up with just the line chart of actual data superimposed on a bar chart of the same actual data? I installed GD::Graph only after reading your question so I don't know much about it -- but I don't see any option for creating a curve. One approach might be to input the actual data points into some kind of algorithm that would create a long series of ordered pairs representing a best-fit curve, and then GD::Graph could plot that. But I don't know how to create such an algorithm. Hopefully someone else here on Daniweb acquainted with statistical analysis modules will reply to your question?

I notice that someone asked a question similar to yours at this link and the response to it sheds some light on the problem but doesn't contain the complete solution.

[d5e5]

Hi David,
Thanks for your promt response.

but this a line curve of actual values.
Plot the data in a bars. Then create a curve over the bar chart. So that gives you 2 bell shaped curve. The curve will be through the center of each bar. Does it make sense?

See this link
http://training.ce.washington.edu/WSDOT/Modules/08_specifications_qa/normal_distribution.htm

Any help is greatly appreciated.

I looked at the example in the link you gave and the curve is not drawn through the centre of each bar. It looks like someone used their intuition to draw a bell curve that best fit the actual data represented by the bars. I doubt that GD::Graph can guess which bell curve best fits a small sample of data points. There may be statistical analysis packages that do this.