A five-number summary is a method of summarizing a dataset by providing a concise description of its key features. It consists of the minimum value, the maximum value, the median, the first quartile, and the third quartile. These five numbers are used to provide a rough sketch of the data and to identify any potential outliers.

For example, let’s say we have a dataset of 100 numbers. We can use the five-number summary to quickly summarize the data and identify any potential outliers. To do this, we would first order the numbers from least to greatest. Then, we would calculate the minimum value, the maximum value, the median, the first quartile, and the third quartile.

The minimum value is the lowest number in the dataset. For our example, the minimum value would be 1.

The maximum value is the highest number in the dataset. For our example, the maximum value would be 100.

The median is the middle number in the dataset when the numbers are ordered from least to greatest. For our example, the median would be 50.

The first quartile is the number that divides the lower half of the dataset into two parts. For our example, the first quartile would be 25.

The third quartile is the number that divides the upper half of the dataset into two parts. For our example, the third quartile would be 75.

We can use these five numbers to quickly summarize the data and identify any potential outliers. For example, if we see a number that is much lower than 1 or much higher than 100, we would know that it is an outlier.

Let’s look at another example to further understand the five-number summary.

Suppose we have a dataset of test scores for a class of 20 students. The scores are as follows:

80, 85, 90, 95, 90, 85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15

To find the five-number summary for this dataset, we would first order the numbers from least to greatest. This would give us the following:

15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 80, 85, 85, 90, 90, 95

Next, we would calculate the minimum value, the maximum value, the median, the first quartile, and the third quartile.

The minimum value is 15.

The maximum value is 95.

The median is 60.

The first quartile is 40.

The third quartile is 85.

Using these five numbers, we can quickly summarize the data and identify any potential outliers. For example, if a student scored a 100 on the test, we would know that this is an outlier because it is much higher than the maximum value of 95.

Overall, the five-number summary is a useful tool for quickly summarizing a dataset and identifying potential outliers. It provides a concise description of the key features of the data and allows us to easily visualize the distribution of the data.