In the other sections on this guide on descriptive statistics, we discussed the concept of percentiles. Specifically, we delved into the different types of percentiles **statisticians** use to investigate their data, how to calculate them and what they are used for. In this section, you’ll find a comprehensive summary of the concept of quartiles.

## Raw Scores

Raw scores can sound like an intimidating concept - after all, what exactly makes a score raw? The definition of a raw score is an unaltered data point. Simple! This typically is a quantitative variable and is called a raw score because it is not transformed or** modified** in any way.

Variable modification comes in many forms and is performed for many reasons. Say, for example, you attain the average speed of cars on a particular street in miles per hour. However, you want to display this mean speed in kilometres per hour - you would then perform a** simple operation** to covert miles per hour into kilometres per hour. The original measure, miles per gallon, is unaltered - in contrast to the transformed measure in kilometres per hour.

In the case of raw scores, this unaltered datapoint or data set typically applies to some sort of score. This would be something like **test scores** for example. However, raw scores don’t have to necessarily be scores in the traditional sense.

Transforming a variable isn’t only executed to ease the interpretation or the spread of information. Transformations to a data set or variable also happen to enable the **comparison** of different data points. One example of this is standardization, where each measure or variable is standardized in order to be able to compare them based off a standard normal distribution.

Transformation | Description | Example |

Change of Units | Performing an operation on a variable or value in order to convert it from one unit to another | Changing the variable of weight from pounds to kilograms |

Creation of a New Variable | Performing an operation on a variable or value in order to create a new variable | Dividing the variable weight from the variable height squared in order to create the variable BMI |

Standardization | Standardizing the data in order to compare datapoints using a standard normal distribution or a z-table | Standardizing the variable of weight in order to compare how extreme values are given the mean and standard deviation |

Percentiles | Splitting the data into percentiles in order to compare different segments of the sample | Splitting the data into quartiles in order to compare each 25% segment of the sample |

As you can see from the table above, there are a couple of basic transformations you can perform on a variable.

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