Important: I don't really know how people generally compute deviations from / , but smth tells me generally it's just a Av Dev/St Dev based on mean, not on appropriate basis, like weighted mean in our case. This version is mathematically correct, it first calculates weighted mean, than utilizes this weighted in mean in AvDev & StDef functions modified to take into account weights.
In true TradingView spirit, the author of this script has published it open-source, so traders can understand and verify it. Cheers to the author! You may use it for free, but reuse of this code in a publication is governed by House Rules. You can favorite it to use it on a chart.