Video: Creating a Data Set given Its Range, Median, and Mode

A set of 4 numbers has a range of 7, a median of 13, and a mode of 16. Given that the highest number is also the mode, what are the four numbers?

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Video Transcript

A set of four numbers has a range of seven, a median of 13, and a mode of 16. Given that the highest number is also the mode, what are the four numbers?

We’re told that there are four numbers in a data set. Let’s consider them in ascending order from left to right. We are told that the mode is 16 and that the highest number is also the mode. As the mode is the most frequently occurring or most common number, we must have two 16s in the last two boxes.

We are told that the median is equal to 13. As the median is the middle value, and there are two middle numbers, each of these must be equidistant from 13. The two numbers in the middle of our data set are 10 and 16 as these have a median of 13. We are told that the range is equal to seven. And this is the difference between the largest and smallest number. 16 minus seven is equal to nine. Therefore, the smallest number is nine. The set of four numbers is nine, 10, 16, and 16.

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