What do you do when you’re lost? You use tools like a compass and GPS to figure out where you are and how to get where you are going. Well, in statistics there are ways to figure out where a data point or set falls. These are called **measures of position**. Once we know where a data set or model is, we can figure out what to do with it. Let’s discuss how we find out where data is and what that means.

## Percentiles

**Percentiles **are common measures of position. To get a percentile, the data is divided into 100 regions. A specific data point will fall in one of those regions and then you assign a percentile to indicate how much data is *below* that specific data point.

For example, I recently took one of my foster children to the doctor and they measured her height (3’4″ if you’d like to know). Once they had her height, they compared it to the national average. In the case of my foster daughter, she is in about the 50% of the national data. This means that she is taller than 50% of girls her age. This means that she is above average.

Percentiles are a good way to express the measure of position for large datasets. Many national assessments, such as height and ACT scores, use percentiles as a way to convey where specific scores fall because they are easily interpreted.

## Quartiles

Quartiles are a nifty way to determine where data fall. Quartiles essentially divide the data into four regions. The first region comprises the lowest point in the data to the median of the lower half of the data. The second quartile region is from the median of the lower half of the data to the median of the entire data set. The third region makes up the data from the median of the entire data set to the median of the upper half of the data. The final region is made up of the data from the median of the upper half to the greatest data point.

The key region is the *interquartile range*. This region represents the middle 50% of the data. Knowing which quartile a datum falls in gives you a sense of how different the data is. It is also a get way to identify outliers, the points that are excessively high or low.

## Z-scores

Z-scores are the most amazing way to identify how a data point differs from the mean. Essentially, a z-score is a measure how much the datum or model differs from a standardized mean. Once you calculate a z-score, you can determine whether it is different enough to be significant. A z-score is calculated as

Since is in terms of standard deviations, it is possible to determine significant difference. For example, a datum of a model with a z-score of ± 1.2 means that the datum differs from the mean by 1.2 standard deviations. If the z-score is ± 2.6, then the datum or model is 2.6 standard deviations from the mean. This means that the datum or model is statistically from the mean and represents a significant result.

## The Takeaways

There are three distinctly different measures of position that you can use to determine the placement of data in a sample. Percentiles represent how much of the data is below a certain point. Quartiles are used to determine how the data falls in comparison to the medians of different sections of the data. Finally, z-scores represent how much the data differs from the mean of the population or sample. I hope that this helps clarify measures of position for you. I look forward to seeing your questions below. Happy statistics!

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