Question

a boxplot was constructed for a data set, but it was later discovered that the maximum value was recorded incorrectly. it should have been 11. 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 \( \text{Range} = \text{Maximum value} - \text{Minimum value} \). Let the original maximum value be \( M_{\text{old}} \) and the corrected maximum value be \( M_{\text{new}} = 41 \). Let the minimum value be \( m \) (which remains unchanged).

Step2: Calculate the change in range

The original range is \( R_{\text{old}} = M_{\text{old}} - m \). The new range is \( R_{\text{new}} = M_{\text{new}} - m \). The increase in range is \( R_{\text{new}} - R_{\text{old}}=(M_{\text{new}} - m)-(M_{\text{old}} - m)=M_{\text{new}} - M_{\text{old}} \). From the boxplot, the original maximum (the end of the right whisker) is at 40. So \( M_{\text{old}} = 40 \) and \( M_{\text{new}} = 41 \). Then the increase is \( 41 - 40 = 1 \).

Answer:

1