Final answer:
To have a range of 6.2 and a median of -5, the value that should appear on the final card is -4.8.
Step-by-step explanation:
To find the value that should appear on the final card in order to have a range of 6.2 and a median of -5, we need to consider the range and the position of the median in the data set.
The range is the difference between the smallest and largest values.
In this case, the range is 6.2. So, we need to find the smallest and largest values in the given set of cards.
The smallest value is -8.6 and the largest value is -3.7.
If we subtract the smallest value from the largest value, we get 6.2. So, the range is satisfied.
The next step is to find the median.
The median is the middle value when the data set is arranged in ascending order.
In this case, the median is -5.
To determine the final card value that would give a median of -5, we need to arrange the cards in ascending order and find the card that is the middle value.
Arranging the cards in ascending order, we have:
-8.6, -7.1, -5.2, -4.8, -3.7, x
The median is the middle value, so it is -5.
Therefore, -4.8 is the value that should appear on the final card.