Question

I have 6 graph bars with the prices.
Each price number will represent its graphbar’s height by respecting min and max heights.
What i want is that graph bar’s height wouldn’t go below or above the min and the max value.

So i have values of min = 55 and max = 110.
And price numbers are:

1. 49
2. 212
3. 717
4. 1081
5. 93

By which mathematical algorithm I could achieve expected results ?
It’s some sort of dynamic scalable bar graphs.

Modified
So the min and max values from the price list will be: 49(min price) => 55(min) and 1081 (max price) => 110(max)

Answer 1

The solution is simple:

• Pick the smallest, and largest item and find the difference.
• (largest_item – smallest_item) maps to (max-min).
• Compute ratio = (max-min)/(largest_item-smallest_item)
• final_value = min_value + ratio*(value-smallest_item)

As a mathematical function:

f(x,max,min,largest,smallest) = min + (max-min)/(largest-smallest)*(x-smallest)
where:
x : Input item's price
max: Maximum value (here, 110)
min: Minimum value (here, 55)
largest: Largest item in input (Here, 1081)
smallest: Smallest item in input (Here, 49)

One check, as @amit correctly points out: Ensure largest and smallest item are distinct.

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So let x = 93. We have other 4 values with us.

f(x,max,min,largest,smallest) = min + (max-min)/(largest-smallest)*(x-smallest)

value = 55  +   ((110-55)/(1081-49)) * (93-49)
value = 57.344961

Further,

f(93,110,55,1081,49) = 57.344961
f(49,110,55,1081,49) = 55
f(1081,110,55,1081,49) = 110