Question

1. a boxplot was constructed for a data set, but it was later discovered that the maximum value was record incorrectly. the value 44 was a mistake and should have been 44.

a by how much does the range of the data increase after making this correction?
increase in range = enter your next step here
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Explanation:

Step1: Recall the formula for range

The range of a data set is calculated as \( \text{Range} = \text{Maximum value} - \text{Minimum value} \). The minimum value here is 4 (from the number line), and initially, the maximum value was 44 (the mistake). After correction, the maximum value should be... Wait, there seems to be a typo in the problem statement (saying "should have been 44" which is the same as the mistake). Assuming it's a typo and the correct maximum should be, say, 49? Wait, looking at the number line, there's 49. Let's re - examine.

Wait, the original maximum was a mistake. Let's assume that the incorrect maximum was 44, and the correct maximum is 49 (from the number line's marking at 49). The minimum value is 4.

Step2: Calculate original range

Original range (with incorrect max) \( R_{original}=44 - 4=40 \).

Step3: Calculate corrected range

Corrected range (with correct max, assuming correct max is 49) \( R_{corrected}=49 - 4 = 45 \).

Step4: Calculate the increase in range

Increase in range \(=\text{Corrected range}-\text{Original range}=45 - 40 = 5 \).

Wait, maybe the mistake was that the original maximum was, for example, if the incorrect value was 44 and the correct one is, let's check the number line. The number line has 4, 39, 44, 49. Let's assume that the original maximum was 44 (wrong) and the correct maximum is 49. Then:

Original range: \( 44 - 4=40 \)

New range: \( 49 - 4 = 49 - 4=45 \)

Increase: \( 45 - 40 = 5 \)

Answer:

5