# Calculate accuracy %

1. Oct 11, 2012

### apostolis22

I have 5 boxes with tools. I made an inventory of the number of the tools that exist in the boxes. I have the results of the inventory but I didnt count the correct number of the tools that were existed in the boxes.

the actual number of the tools is:

box 1 = 5 tools
box 2 = 4 tools
box 3 = 8 tools
box 4 = 9 tools
box 5 = 7 tools

the inventory is :

box 1 = 6 tools
box 2 = 7 tools
box 3 = 6 tools
box 4 = 8 tools
box 5 = 8 tools

How can I calculate the accuracy % of the inventory referred to the actual number of the tools (per box and summary number) ?

Thank you!

2. Oct 11, 2012

### haruspex

There is no standard way to define accuracy on a 0 to 100% scale in such a situation. You could try making up your own definition. There are certain axioms you need it to satisfy. if you think of it as a proximity measure in a some kind of vector space, you could start with a metric, d(x,y), satisfying the usual axioms for those, then convert it to a proximity measure p, e.g. p = exp(-d)*100%

3. Oct 11, 2012

### apostolis22

I quite understood what you ment . I want to calculate the accuracy of the inventory in excel. Could you make an a example of this please? :)

4. Oct 11, 2012

### haruspex

You could take the metric (d) as sum of squares of differences, or the square root of that. But you might feel you want to normalise it in relation to the magnitude of the correct values, e.g. (4, 6) is the same distance from a correct answer of (2, 8) as (2, 3) would be from a correct answer of (1, 4). To achieve that, divide the root sum square of the difference by the standard deviation of the target vector elements.
Then convert to an accuracy measure by any monotonic function that maps 0 to 100% and infinity to 0, e.g. Exp(-d).