side-by-side box-and-whisker plots can be used to compare two or more different data sets. each box-and-whisker plot is drawn on the same number line to compare the data sets more easily. the lengths (in seconds) of songs from two different concerts are shown. complete parts a through d below.

(a) describe the shape of each distribution. which concert has less variation in song lengths?

the distribution of concert 1 is skewed left.
the distribution of concert 2 is symmetric.

which concert has less variation in song lengths?
dropdown has less variation in song lengths.
concert 1
concert 2

Question

side-by-side box-and-whisker plots can be used to compare two or more different data sets. each box-and-whisker plot is drawn on the same number line to compare the data sets more easily. the lengths (in seconds) of songs from two different concerts are shown. complete parts a through d below.

(a) describe the shape of each distribution. which concert has less variation in song lengths?

the distribution of concert 1 is skewed left.
the distribution of concert 2 is symmetric.

which concert has less variation in song lengths?
dropdown has less variation in song lengths.
concert 1
concert 2

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Box Plot Symmetry", "Distribution Shape Analysis", "Measures of Variation", "Range Calculation", "Interquartile Range" ], "new_concepts": [], "current_concepts": [ "Box Plot Symmetry", "Distribution Shape Analysis", "Measures of Variation", "Range Calculation", "Interquartile Range" ] } ## Compare the ranges of both distributions Using the *Range Calculation* knowledge point $$ \begin{aligned} &\text{Range}_{\text{Concert 1}} = 333 - 163 = 170\ &\text{Range}_{\text{Concert 2}} = 247 - 184 = 63 \end{aligned} $$ ## Compare the interquartile ranges of both distributions Using the *Interquartile Range* knowledge point $$ \begin{aligned} &\text{IQR}_{\text{Concert 1}} = 310 - 256 = 54\ &\text{IQR}_{\text{Concert 2}} = 228 - 202 = 26 \end{aligned} $$ ## Determine which concert has less variation Using the *Measures of Variation* knowledge point $$ \begin{aligned} &\text{Range}_{\text{Concert 2}} < \text{Range}_{\text{Concert 1}} \quad (63 < 170)\ &\text{IQR}_{\text{Concert 2}} < \text{IQR}_{\text{Concert 1}} \quad (26 < 54) \end{aligned} $$ Therefore, Concert 2 has less variation in song lengths.

Concert 1

Concert 2

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Measures of Variation" ] }

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QUESTION IMAGE

Question

Explanation:

Compare the ranges of both distributions

Compare the interquartile ranges of both distributions

Determine which concert has less variation

Answer: