javascript - Math: I need to normalize some bar graphs - Stack Overflow

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I'm generating bar graphs. The range of data generating said graphs is very wide, which means some areas of the graph are always low, and some areas go off the chart.

What's the math to "normalize" this towards a certain number (e.g. 200), so large values are shrunk the larger they are, and smaller values are increased?

I'm generating bar graphs. The range of data generating said graphs is very wide, which means some areas of the graph are always low, and some areas go off the chart.

What's the math to "normalize" this towards a certain number (e.g. 200), so large values are shrunk the larger they are, and smaller values are increased?

• javascript
• math

Share Improve this question Follow edited Dec 31, 2012 at 7:41 HebeleHododo 3,63611 gold badge3131 silver badges3939 bronze badges asked Dec 31, 2012 at 7:39 Erik NelsonErik Nelson 1,01944 gold badges1212 silver badges1313 bronze badges 4

• Oh, this is in javascript, sorry! – Erik Nelson Commented Dec 31, 2012 at 7:40
• your stackoverflow reputation can be seen as a graph... which can be pretty sparse, do you want something like that ? And in which programming language ....? – AurA Commented Dec 31, 2012 at 7:43
• Could you not find the highest value and use % in relation to that for all the bars – Sir Commented Dec 31, 2012 at 8:00
• 2 What about the logarithmic scale? – John Dvorak Commented Dec 31, 2012 at 8:13

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4 Answers 4

Sorted by: Reset to default 8

If you are talking about actually changing the data for display purposes, then there are a few basic approaches to bring values closer to a target value. The simplest is to just do a weighted average with that value: A' = (1-α)*A + α*B where alpha is a weight between 0 and 1, A is a number on your graph, and B is the target value.

For instance, if you were trying to 'normalize' to 200 and your numbers were 100 120 200 220 400 then plugging in each for A, 200 for B, and .5 for alpha, you would get 150 160 200 210 300

You can choose a different alpha to adjust how much you want to stretch the data towards the target value. Higher numbers like .9 will stretch the data more and lower numbers like .1 will stretch the data less.

I dont know if you are willing to read a little but I found the the scaling tutorial for d3.js framework (http://d3js/) is a very solid introduction to the scaling part of visualisation:

http://alignedleft./tutorials/d3/scales/

For a zero-based graph : pute the max of your value, then display for each bar :

barHeight[i] = (maxBarHeight*value[i])/maxVal;  

If you want your graph to be based on the minimum value and not zero, you might still want the graph to have a non-zero height for the bar near the min value. So pute the minimum value, and display :

 barHeight[i] = minBarHeight + 
         (maxBarHeight - minBarHeight ) * (value[i] - minVal) / ( maxVal - minVal );

( Rq : if minVal is Zero or 'near' zero, set minVal = minBarHeigth = 0 and you have the first case )

One could take the data set and find the standard deviation. This naturally demarks seven distinct points that we can use to define the spans that the bars can be drawn up to. One can even take the standard deviations of subsets of data that fall into initial spans in order to further demark points along the bar.

E.G.

We have a function 'barBuilder' that can call the function 'rightHand' and 'leftHand'. We are traversing a key, value pair map of a word onto a frequency. We have the standard deviations and mean value for our frequency cached with respect to our data set; and we are ready to paint our bar for each key.

We will draw the bar only as far from the mean as the frequency indicates it is, where our origin is the leftmost standard deviation, drawn by 'leftHand', up to the highest standard deviation that we have fit to our model, drawn by 'rightHand'.

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