Step-by-step explanation:
To find the minimum value of the range of six different natural numbers with a median of 7, let's consider the properties of medians in sets of numbers.
If the median of the set is 7 and the numbers are different natural numbers, then the set of numbers must be symmetrically distributed around the median.
For six numbers in ascending order, the middle two numbers will be the median values. As the median is 7, these two middle numbers are 7 and 7.
To have six different natural numbers with 7 as the median, we can consider the smallest possible natural numbers less than 7 and the largest possible natural numbers greater than 7.
The minimum values less than 7: 1, 2, 3, 4, 5
The maximum values greater than 7: 8, 9, 10, 11, 12
Therefore, the smallest natural number set that fits the criteria with a median of 7 would be: 1, 2, 5, 7, 10, 12
The range of this set of numbers = Maximum value - Minimum value
Range = 12 - 1 = 11
Hence, the minimum value of the range of six different natural numbers with a median of 7 is 11.
