### Video Transcript

The grades of six students in two different mathematics tests are reviewed. The range of the students’ grades in the first test is five. Find the range of their grades in the second test if they scored 18, 22, 23, 25, 26, and 27. What can we conclude from the ranges about the spread of the grades in the two tests?

In this question, we are told that six students sit two different tests. We aren’t given the individual grades in the first test, but we are told that the range is five. In the second test, we have the six individual grades, and we need to calculate the range of these scores.

The range gives us a spread of data. And it’s calculated by the largest data value subtract the smallest data value. The largest data value in this set is 27, and the smallest is 18. These scores are helpfully given in order from the smallest to the largest, but they don’t need to be. We just find the largest and the smallest. And so when we calculate 27 take away 18, we get a range of nine. And so that’s the first part of the question answered.

In the second part of the question, we need to draw a conclusion about the spread of the data from the ranges. We were told that the first test has a range of five, and we’ve just worked out that the second test has a range of nine. When the range is larger, the spread is larger. And when the range is smaller, the spread is smaller. Therefore, we need to give a statement which shows that we understand this, something like the spread of the grades in the first test is smaller than the spread of the grades in the second test.

The information about the range or the spread of the data might be useful for a teacher to know. For example, if a range of scores is small in a test paper, then that means that students are mostly working at the same level and have the same level of understanding. However, if there is a larger range in the test scores, then that means that some or one student will know a lot less or even more than the others.