## Example

## Generic Formula

**Note**: This is an **array formula**. Do not type out the **{}** brackets. Hold **Ctrl** + **Shift** then press **Enter** while in **Edit Mode** to create an **array formula**.

**Range** – This is the range of values which you would like to sum all odd numbers from.

## What It Does

This formula will sum all the odd numbers from a given range of values. An odd number is defined as any number that has a remainder of 1 when divided by 2.

## How It Works

The **MOD** function returns the remainder of a number on division by another number. For example **MOD(7,2)** will return **1** since the remainder of 7 divided by 2 is 1. We use the **MOD** function to test if a number is odd. A number will be odd if and only if the remainder on division by 2 equals 1. In other words, **N** is odd if and only if **MOD(N,2)=1**.

**MOD(Range,2)=1** will create an array of Boolean values where **TRUE** will mean the number is odd and **FALSE** will mean the number is not odd. We then multiply this Boolean array by the **Range** to get an array where each value is either an odd value from the **Range** or a **0**. This is because N*TRUE equals N and N*FALSE equals 0 for any number N.

In our example **MOD({1.36;-2;2;9;10;7;1.33;8},2)=1** will result in the following Boolean array.

When we multiply this by **Range** we get **{0;0;0;9;0;7;0;0}**. Then **SUM({0;0;0;9;0;7;0;0})** results in **16** which is the sum of all odd numbers in our range of values.