Question

measures of spread - range - item 4823
study the data set shown. then answer the questions below.
53 54 63 63
68 68 68 74
82 85 85 88
89 92 92 97
enter a number that could be removed from this data set that would not change the range.
enter a number that could be removed from 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. First, identify the minimum and maximum values in the data set. The data set is: 53, 54, 63, 63, 68, 68, 68, 74, 82, 85, 85, 88, 89, 92, 92, 97. The minimum value ($min$) is 53 and the maximum value ($max$) is 97. So the range is $97 - 53 = 44$.

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

A number that is neither the minimum nor the maximum can be removed without changing the range. For example, let's take 63. If we remove 63, the new data set still has minimum 53 and maximum 97, so the range remains $97 - 53 = 44$. (Other numbers like 54, 68, 85, 92 etc. which are not min or max can also be chosen.)

Step3: Determine a number that changes the range when removed

If we remove the minimum (53) or the maximum (97), the range will change. Let's take 53. If we remove 53, the new minimum will be 54 (since 53 was the smallest). The maximum is still 97, so the new range is $97 - 54 = 43$, which is different from the original range. Similarly, removing 97 will change the maximum and thus the range.

Answer:

First blank (number that doesn't change range): 63 (or other non - min, non - max numbers like 54, 68, 85, 92 etc.)
Second blank (number that changes range): 53 (or 97)