Final answer:
Changing the metabolic rate value from 1772 to 1972 does not affect the median of the ordered set, which remains 1614, as this change does not affect the position of the middle number.
Step-by-step explanation:
The original set of metabolic rates is 1772, 1666, 1362, 1460, 1867, 1439, and 1614. To find the median, we would first order the numbers from least to greatest: 1362, 1439, 1460, 1614, 1666, 1772, and 1867. The median in this set is 1614 because it is the middle number when the data is ordered sequentially.
If the number 1772 is accidentally changed to 1972, the new set of numbers will be 1362, 1439, 1460, 1614, 1666, 1972, and 1867. When we reorder these values, the set becomes 1362, 1439, 1460, 1614, 1666, 1867, and 1972. The new median of this set is still 1614, as changing the value of 1772 to 1972 does not affect the position of the middle number.
Therefore, changing the number 1772 to 1972 would not change the value of the median.