Question

study the data set shown. then answer the questions below.
42 50 51 53 55
56 56 57 57 57
59 60 60 61 63
64 64 66 66 68
enter a number that could be added to this data set that would not change the range.
enter a number that could be added to this data set that would change the range.

Explanation:

Step1: Find the range of the data set

The range is calculated as the maximum value minus the minimum value. In the data set, the minimum value is \( 42 \) and the maximum value is \( 68 \). So the range is \( 68 - 42 = 26 \).

Step2: Determine a number that doesn't change the range

A number that is between the minimum (\( 42 \)) and maximum (\( 68 \)) (inclusive) will not change the range. For example, \( 50 \) is within this interval.

Step3: Determine a number that changes the range

A number less than the minimum (\( 42 \)) or greater than the maximum (\( 68 \)) will change the range. For example, \( 70 \) is greater than \( 68 \), so adding it will change the range.

Answer:

For the first blank (no change to range): \( 50 \) (any number between 42 and 68 inclusive is correct)
For the second blank (change to range): \( 70 \) (any number less than 42 or greater than 68 is correct)