Question

a boxplot was constructed for a data set, but it was later discovered that the maximum value was recorded incorrectly. the value 49 was a mistake and should have been 91. by how much does the range of the data increase after making this correction?

Explanation:

Step1: Recall the formula for range

The range of a data set is calculated as \( \text{Range} = \text{Maximum value} - \text{Minimum value} \).

Step2: Calculate the change in maximum value

The original maximum value was \( 49 \), and the corrected maximum value is \( 94 \). The change in the maximum value is \( 94 - 49 = 45 \).

Step3: Determine the change in range

Since the minimum value remains unchanged (only the maximum value is corrected), the increase in the range is equal to the increase in the maximum value. So the range increases by \( 45 \).

Answer:

The range of the data increases by \( 45 \).