Questions: Which of the following statements are false regarding a boxplot? Boxplots can be used to either describe a single variable in a data set or to compare two (or more) variables The right and left of the box are the third and first quartiles The length of the box equals the range of the data. The height of the box has no significance.

Which of the following statements are false regarding a boxplot? Boxplots can be used to either describe a single variable in a data set or to compare two (or more) variables The right and left of the box are the third and first quartiles The length of the box equals the range of the data. The height of the box has no significance.
Transcript text: Which of the following statements are false regarding a boxplot? Boxplots can be used to either describe a single variable in a data set or to compare two (or more) variables The right and left of the box are the third and first quartiles The length of the box equals the range of the data. The height of the box has no significance.
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Solution

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Solution Steps

To determine which statements are false regarding a boxplot, we need to understand the properties of a boxplot. A boxplot is a graphical representation of data that shows the distribution through their quartiles. The box represents the interquartile range (IQR), which is the distance between the first quartile (Q1) and the third quartile (Q3). The length of the box is the IQR, not the range of the data. The height of the box is not significant as boxplots are typically horizontal. We will evaluate each statement based on these properties.

Step 1: Understanding Boxplot Properties

A boxplot is a graphical representation that summarizes the distribution of a dataset through its quartiles. The box itself represents the interquartile range (IQR), which is defined as the distance between the first quartile \( Q_1 \) and the third quartile \( Q_3 \). The length of the box is given by \( IQR = Q_3 - Q_1 \).

Step 2: Evaluating the Statements

  1. Statement 1: "Boxplots can be used to either describe a single variable in a data set or to compare two (or more) variables."
    This statement is true as boxplots are versatile in representing both single and multiple variables.

  2. Statement 2: "The right and left of the box are the third and first quartiles."
    This statement is also true; the left side of the box corresponds to \( Q_1 \) and the right side corresponds to \( Q_3 \).

  3. Statement 3: "The length of the box equals the range of the data."
    This statement is false. The length of the box represents the IQR, not the total range of the data, which is defined as \( \text{Range} = \text{max} - \text{min} \).

  4. Statement 4: "The height of the box has no significance."
    This statement is true in the context of horizontal boxplots, where the height does not convey additional information.

Step 3: Identifying False Statements

From the evaluation, the only false statement is:

  • "The length of the box equals the range of the data."

Final Answer

The false statement is: \\(\boxed{\text{"The length of the box equals the range of the data."}}\\)

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