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Determining the Median of a Set of Numbers

To find the median of a given set of numbers, we first need to arrange the numbers in ascending order. The numbers provided are:

Step 1: Arrange the Numbers

Let's start by sorting the numbers in ascending order:

  1. 65
  2. 72
  3. 77
  4. 85
  5. 88
  6. 91

Now that we have the numbers arranged, we can move on to find the median.

Step 2: Calculate the Median

The median is defined as the middle value of a data set when the numbers are arranged in order. The method for finding the median differs depending on whether the number of observations (in this case, the total count of numbers) is odd or even.

In our case, there are 6 numbers in the set, which is an even number. To find the median for an even set, we take the two middle numbers and calculate their average.

Identifying the Middle Numbers

The two middle numbers in our sorted list are:

Step 3: Calculate the Average of the Middle Numbers

We will now calculate the average of 77 and 85:

[ \text{Median} = \frac{77 + 85}{2} = \frac{162}{2} = 81 ]

Conclusion

In conclusion, the median of the set of numbers 72, 85, 91, 77, 65, and 88 is 81.