If we use the range to measure variability, we say the distributions have the same amount of variability. But the variability in the distributions differ when we look at how the data is distributed about the median. Set A has a large portion of its data close to the median. This is not true for Set B. From this viewpoint, Set A has less variability about the median. Now we develop a way to measure the variability about the median. To do so, we use quartiles.
Quartile marks divide the data set into four groups with equal counts. We added dividers to show the quartile marks for the two sets of exam scores. Apply market research to generate audience insights.
Measure content performance. Develop and improve products. List of Partners vendors. Share Flipboard Email. Courtney Taylor. Professor of Mathematics. Courtney K. Taylor, Ph. Updated January 26, Featured Video.
Cite this Article Format. Taylor, Courtney. Understanding the Interquartile Range in Statistics. When the sample size is odd, the median and quartiles are determined in the same way. The median and quartiles are indicated below. When the sample size is 9, the median is the middle number The quartiles are determined in the same way looking at the lower and upper halves, respectively.
When there are no outliers in a sample, the mean and standard deviation are used to summarize a typical value and the variability in the sample, respectively. When there are outliers in a sample, the median and interquartile range are used to summarize a typical value and the variability in the sample, respectively. There are several methods for determining outliers in a sample. A very popular method is based on the following:. Outliers are values below Q 1 Measures of Spread or Variation Recall the five-number summary from Example 3.
Table 3. Dotplot of Salaries What you notice in Figure 3. This is because sensitive measures tend to overreact to the presence of outliers. If a sample is reasonably symmetric, sensitive measures should be used.
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