I transform the tip amount (in $) to % and it doesn't match the tips- Can someone Explain?

[Shirlybl]

Hi Everyone! 

Can someone explain the following weird phenomena? I am trying to understand if my tipping system works and to do some stats to see how many consumers choose each of my tipping options.  

I transform the tip (in $) to % out of total bill amount and most of the transactions do not match the 3 tip options the consumers saw. For example, my system shows tips options as 10%-15%-20% but when I look at the frequencies of tips, the % shows that people tipped 9.95%, 9.96%, 9.97%...10% etc meaning that either most of the consumers do not even click one on the options provided (nut maybe clicked custom tip which is unlikely) or that there is a deviation in the system.

PS- my POS include the tip after the tax so to compute the tip as % I did- tip/ (gross sale+tax)

Does anyone have a clue of what is this?  

[RHatch]

This is due to rounding.  For example if my Sale with tax was $10.00 and my tip was 10% or $1.00 then when I calculate this forward and back it is the same because there is no rounding.  However, if my sale is $10.51 with a 10% tip the tip ammount is not $1.05 but $1.051.  Rounding to a 2 digit decimal place does not give us an event percentage.

So if I take the tip rounded  $1.05 /  Gross Sale $10.51 X 100 I get 9.99%,  but if I take $1.051 / $10.51 X 100 I get 10%

So because your tip $ are rounded you need to round your percentage calculations.