When analyzing data sets, the first thing to identify is the maximums, minimums, and outliers. This lesson will help you learn how to identify these important items.

## Finding Maximums, Minimums & Outliers

Bob, of Bob’s Used Cars, is looking at the car sales for the past year. He wants to create a promotional sale during the slowest car sales month. He also wants to see if there are any other months that stand out in sales.A good way for Bob to analyze his car sales data is to identify the minimum, maximum and outliers in the data set. Take a look at the data set that Bob put together for the year of car sales. This is the data set we will be working with to find the maximum, minimum and outlier.The **maximum** value in the data set is the largest mathematical value in the data set.

The **minimum** value in the data set is the smallest mathematical value in the data set. An **outlier** is a value that is much larger or smaller than the other values in a data set, or a value that lies outside the given data set.First, we need to order the data from least to greatest value, like this:10, 19, 20, 21, 22, 22, 23, 24, 24, 25, 26, 26.The minimum value is 10 in this data set, as it is the smallest number. The maximum value is 26, as it is the largest number.

Now take a look at both the minimum and maximum values. You’ll notice that with the maximum value we have two 26s, and then the numbers descend by 1, down to 25, 24, 23 and so on. Therefore, the maximum value is not an outlier, because the number 26 is not significantly larger than the other numbers near it in the data set.

However, you may notice that with the minimum value, the data set jumps from 10 to 19. There is a difference of 9 between the two values, which is greater than any other difference in the numbers in the data set. Therefore, we can identify 10 as both the minimum value and as the outlier.

It is important to note here that your outlier will always be either your minimum or maximum value; you cannot have an outlier that is in the middle of the data set.

## Practice Example

Bob wants to analyze the data of his sales staff. He wants to send his lowest salesperson to training and give a bonus to his top salesperson. Bob also wants to see if there are any salespeople that are significantly under-performing. First, let’s order this data from least to greatest: 50, 52, 53, 67, 80.

Okay, so the minimum and maximum values should be pretty easy to identify. Our maximum value here is 80, and our minimum value is 50. Bob decides to send Jim to sales training, and he gives a bonus to Sally, because he doesn’t want to give the bonus to himself.We do have an outlier in this data set, which is 80.

80 is far apart from the next number, 67, whereas 50, 52 and 53 are relatively close together. Therefore, we can say that Bob does not have any employees that are significantly under-performing.

## Lesson Summary

Bob used the maximum and minimum values to analyze his sales data. The **maximum value** in the data set is the largest mathematical value in the data set. The **minimum value** in the data set is the smallest mathematical value in the data set.The minimum and maximum values can also be the outliers.

An **outlier** is a value that is much larger or smaller than the other values in a data set, or a value that lies outside the given data set. Remember that an outlier will always be the minimum and/or maximum values.In the examples we saw, the first data set had an outlier of 10 – that was the minimum value – and the second data set had an outlier of 80, which was the maximum value.

You can also have a data set with two outliers, both the minimum and the maximum values.

## Learning Outcome

At the end of this lesson, you should be able to identify the maximum, minimum, and outlier values of a data set for analysis.