Question

Look at this set of 9 numbers:
4 8 2 6 6 3 6 3 8
By how much would the range decrease if the number 2 were added to the set?

Answer 1

To find the range of the original set of numbers, we need to identify the maximum and minimum values in the set:

- The original set is: 4, 8, 2, 6, 6, 3, 6, 3, 8.
- The maximum value is 8.
- The minimum value is 2.

The range is calculated as:

\[
\text{Range} = \text{Maximum} - \text{Minimum} = 8 - 2 = 6.
\]

Now, let's consider the new set if we add the number 2:

- The new set will be: 4, 8, 2, 6, 6, 3, 6, 3, 8, 2.
- The maximum value remains 8.
- The minimum value remains 2 (as 2 is already in the set).

The range for the new set is:

\[
\text{New Range} = \text{Maximum} - \text{Minimum} = 8 - 2 = 6.
\]

Since both the original range and the new range are 6, the decrease in the range when adding the number 2 is:

\[
\text{Decrease in Range} = \text{Original Range} - \text{New Range} = 6 - 6 = 0.
\]

Therefore, the range does not decrease at all.

The answer is that the range decreases by **0**.