select the correct answer.

sharla wanted to know how many minutes per hour a radio station typically plays music. she collected the following data from seven radio stations.

by how many minutes would her median time change if she added another radio station playing 37 minutes?

0.5
0.4
the median did not change
0.45

Question

select the correct answer.

sharla wanted to know how many minutes per hour a radio station typically plays music. she collected the following data from seven radio stations.

by how many minutes would her median time change if she added another radio station playing 37 minutes?

0.5
0.4
the median did not change
0.45

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Data Interpretation", "Line Plots" ], "new_concepts": [ "Median Calculation", "Data Distribution Changes" ], "current_concepts": [ "Data Interpretation", "Line Plots", "Median Calculation", "Data Distribution Changes" ] } ## Find the initial median $$ \begin{aligned} &\text{Initial dataset: } \{30, 31, 31, 34, 35, 36, 37\} \ &N = 7 \ &\text{Median position: } \frac{7+1}{2} = 4\text{th value} \ &\text{Initial median} = 34 \end{aligned} $$ ## Find the new median $$ \begin{aligned} &\text{New dataset: } \{30, 31, 31, 34, 35, 36, 37, 37\} \ &N = 8 \ &\text{Median position: average of } 4\text{th and } 5\text{th values} \ &\text{New median} = \frac{34 + 35}{2} = 34.5 \end{aligned} $$ ## Calculate the change in median $$ \begin{aligned} &\text{Change} = 34.5 - 34 = 0.5 \end{aligned} $$

(A) 0.5

(B) 0.4

(C) the median did not change

(D) 0.45

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

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QUESTION IMAGE

Question

Explanation:

Find the initial median

Find the new median

Calculate the change in median

Answer: