Question

the depths (in inches) at which 10 artifacts are found are listed.
34.3 28.2 30.8 37.3 45.1 37.2 26.1 36.9 28.7 32.5
the range of the given data set is 19.0. if the current maximum, 45.1, is replaced with 59.1, the range then becomes 33.0. compare these values and determine how outliers affect the range of a data set.
how does changing the maximum value affect the range?
a. the range is greatly affected by this change.
b. the range of a data set depends on the number of data, not the specific values. therefore, the range does not vary by changing the maximum value.
c. the change in the range is low and insignificant.
d. the range becomes more accurate when the maximum value is an outlier.

Explanation:

Analyze the given data and range values

Using the Range Calculation knowledge point

$$
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Evaluate the impact of outliers on the range

The range is calculated using only the maximum and minimum values of a dataset:

$$ \text{Range} = \text{Maximum} - \text{Minimum} $$

Because it relies solely on these two extreme values, any change to the maximum or minimum (such as introducing an outlier) directly and significantly alters the range. In this case, replacing the maximum value increased the range by over \(73\%\), demonstrating that the range is highly sensitive to extreme values and outliers. Therefore, the range is greatly affected by this change.

Answer:

• (A) The range is greatly affected by this change. (Correct answer)
• (B) The range of a data set depends on the number of data, not the specific values. Therefore, the range does not vary by changing the maximum value.
• (C) The change in the range is low and insignificant.
• (D) The range becomes more accurate when the maximum value is an outlier.