Measures of position let you determine the position of a value in relation to other values in a dataset. Along with center and spread, it’s helpful to know the relative position of your values. For example, whether one value is higher or lower than another, or whether a value falls in the lower, middle, or upper portion of your dataset.
In this reading, you’ll learn more about the most common measures of position: percentiles and quartiles. You’ll also learn how to calculate the interquartile range, and use the five number summary to summarize your data.
A percentile is the value below which a percentage of data falls. Percentiles divide your data into 100 equal parts. Percentiles give the relative position or rank of a particular value in a dataset.
For example, percentiles are commonly used to rank test scores on school exams. Let’s say a test score falls in the 99th percentile. This means the score is higher than 99% of all test scores. If a score falls in the 75th percentile, the score is higher than 75% of all test scores. If a score falls in the 50th percentile, the score is higher than half, or 50%, of all test scores.
Percentiles are useful for comparing values and putting data in context. For example, imagine you want to buy a new car. You’d like a midsize sedan with great fuel economy. In the United States fuel economy is measured in miles per gallon of fuel, or mpg. The sedan you’re considering gets 23 mpg. Is that good or bad? Without a basis for comparison, it’s hard to know. However, if you know that 23 mpg is in the 25th percentile of all midsize sedans, you have a much clearer idea of its relative performance. In this case, 75% of all midsize sedans have a higher mpg than the car you’re thinking about buying.
You can use quartiles to get a general understanding of the relative position of values. A quartile divides the values in a dataset into four equal parts.
Three quartiles divide the data into four quarters. Quartiles let you compare values relative to the four quarters of data. Each quarter includes 25% of the values in your dataset.
The first quartile, Q1, is the middle value in the first half of the dataset. Q1 refers to the 25th percentile. 25% of the values in the entire dataset are below Q1, and 75% are above it.
The second quartile, Q2, is the median of the dataset. Q2 refers to the 50th percentile. 50% of the values in the entire dataset are below Q2, and 50% are above it.
The third quartile, Q3, is the middle value in the second half of the dataset. Q3 refers to the 75th percentile. 75% of the values in the entire dataset are below Q3, and 25% are above it.
For example, imagine you’re a data professional working for an auto dealership. The manager of the sales team wants to compare the performance of each sales representative on the team. The manager asks you to analyze data that provides how many cars each sales representative sold during the past month.
You can calculate quartiles for your data in four steps:
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