# SUM\_PRODUCT

### **Description**

`SUM_PRODUCT` takes two lists, multiplies the values in one list with values that are on the same index in the other list. It then adds up those multiplications, resulting in a single new value.

If the two lists within the brackets are of different size, `SUM_PRODUCT` will operate on all values with the same index and ignore all the values of the larger list that exceed the largest index of the smaller list.

###

### **Example: Two list with same length**

In this examples two lists of three values each are used. 

```
SUM_PRODUCT([1, 2, 3], [10, 20, 30])
```

The calculation SUM\_PRODUCT performs is `1*10 + 2*20 + 3*30` and would return `140`.

### Example: List with different length

```
SUM_PRODUCT([1, 2, 3, 999], [10, 20, 30])
```

In this example, the first list has four elements while the second list has only three elements. The extra element `999` of the first list will therefore be ignored and, just as in the example before, `140` will be returned as result. 

### Example: Weighted Risk

Say the overall risk factor of a client is a number calculated from five individual risk factor numbers. Each individual risk factor is given a certain weight in the overall calculation, depending on how impactful we think that factor is.

| Risk Factors    | Weight |
| --------------- | ------ |
| risk\_factor\_1 | 4      |
| risk\_factor\_2 | 2      |
| risk\_factor\_3 | 5      |
| risk\_factor\_4 | 1      |
| risk\_factor\_5 | 3      |

To calculate the overall risk score using `SUM_PRODUCT`, each individual risk factor score will be multiplied by its weight. The results are then summed up and returned as a single value.

```
p is Person
SUM_PRODUCT(
    [
        p.risk_factor_1,
        p.risk_factor_2,
        p.risk_factor_3,
        p.risk_factor_4,
        p.risk_factor_5
    ],
    [4, 2, 5, 1, 3]
)
```

For the table above, if we assume a `Person p` has a set of `risk_factors` with the following corresponding values 3, 6, 2, 8, and 5, the returned result would be 57.