{"status": "success", "data": {"description_md": "Melanie computes the mean $\\mu$, the median $M$, and the modes of the $365$ values that are the dates in the months of $2019$. Thus her data consist of $12$ $1\\text{s}$, $12$ $2\\text{s}$, . . . , $12$ $28\\text{s}$, $11$ $29\\text{s}$, $11$ $30\\text{s}$, and $7$ $31\\text{s}$. Let $d$ be the median of the modes. Which of the following statements is true?\n\n$\\textbf{(A) } \\mu < d < M \\qquad\\textbf{(B) } M < d < \\mu \\qquad\\textbf{(C) } d = M =\\mu \\qquad\\textbf{(D) } d < M < \\mu \\qquad\\textbf{(E) } d < \\mu < M$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Melanie computes the mean  <span class=\"katex--inline\">\\mu</span> , the median  <span class=\"katex--inline\">M</span> , and the modes of the  <span class=\"katex--inline\">365</span>  values that are the dates in the months of  <span class=\"katex--inline\">2019</span> . Thus her data consist of  <span class=\"katex--inline\">12</span>   <span class=\"katex--inline\">1\\text{s}</span> ,  <span class=\"katex--inline\">12</span>   <span class=\"katex--inline\">2\\text{s}</span> , . . . ,  <span class=\"katex--inline\">12</span>   <span class=\"katex--inline\">28\\text{s}</span> ,  <span class=\"katex--inline\">11</span>   <span class=\"katex--inline\">29\\text{s}</span> ,  <span class=\"katex--inline\">11</span>   <span class=\"katex--inline\">30\\text{s}</span> , and  <span class=\"katex--inline\">7</span>   <span class=\"katex--inline\">31\\text{s}</span> . Let  <span class=\"katex--inline\">d</span>  be the median of the modes. Which of the following statements is true?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } \\mu &lt; d &lt; M \\qquad\\textbf{(B) } M &lt; d &lt; \\mu \\qquad\\textbf{(C) } d = M =\\mu \\qquad\\textbf{(D) } d &lt; M &lt; \\mu \\qquad\\textbf{(E) } d &lt; \\mu &lt; M</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "2019 AMC 12A Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc12A_p08", "prev": "/problem/19_amc12A_p06"}}