By normalizing the data we mean scaling the given data values in such a way that all of the given data values lie within the range 0 to 1. The data is scaled proportionally in such a way that the smaller data values lie closer to zero and the larger data values lie closer to 1.

**Steps to Normalize Data in the 0 to 1 Range:**

- Identify the smallest and largest values in the data set.
- Find the range of the given set of data values. This can be done by subtracting the smallest observation from the largest observation. \text{Range } = \text{Largest Observation } - \text{Smallest Observation}.
- Take the difference of each value from the smallest observation.
- Divide each of the above differences by the value of the range of the data set. The resulting numerical values are the normalized data values that always lie between zero and one.

**Formula to Normalize Data between 0 and 1:**

The normalized data values can be calculated using the formula, \text{Normalized Data Values } = \frac{\text{Given Value } - \text{Smallest Value}}{\text{Largest Value} - \text{Smallest Value}}.

**Example 1:**

Consider the following 6 data values: 12, 22, 34, 45, 57, 62.

** Step 1**: The highest and the lowest values are clearly 62 and 12 respectively.

** Step 2**: Therefore the range of the data set is equal to 62 – 12 = 50.

** Step 3**: We now subtract the smallest value 12 from each of the given data values and obtain the following: 0, 12, 22, 33, 45, 50.

** Step 4**: We now divide each of the above numbers by the range 50. The normalize data values are as follows : 0, 0.25, 0.44, 0.66, 0.9, 1.

We can also simply apply the formula directly to compute the normalized values in a single step.

**Example 2:**

Find the normalized data values of the given set of numbers by applying the formula: 112, 156, 194, 204, 312.

The normalized data values can be found as follows, \begin{align*}\text{Normalized Data Values } &= \frac{\text{Given Value}(x) - \text{ Smallest Value}}{\text{Largest Value} - \text{Smallest Value}} \\ &= \frac{ x - 112}{312 - 112} = \frac{ x - 112}{200}.\end{align*}

The normalized data values are now obtained as below,

Data Values (x) | Normalized Data Value = \frac{ x - 112}{200} |

112 | (112 – 112)/200 = 0 |

156 | (156 – 112)/200 = 44/200 = 0.22 |

194 | (194 – 112)/200 = 82/200 = 0.41 |

204 | (204 – 112)/200 = 92/200 = 0.46 |

312 | (312 – 112)/200 = 200/200 = 1 |

**Further Reading:**