median of 3,8,4,6,3,10,7,3,7,7

{ "query": { "display": "median $$3,\\:8,\\:4,\\:6,\\:3,\\:10,\\:7,\\:3,\\:7,\\:7$$", "symbolab_question": "STATISTICS#median 3,8,4,6,3,10,7,3,7,7" }, "solution": { "level": "PERFORMED", "subject": "Statistics", "topic": "median", "subTopic": "Other", "default": "6.5" }, "steps": { "type": "interim", "title": "Median of $$3,\\:8,\\:4,\\:6,\\:3,\\:10,\\:7,\\:3,\\:7,\\:7:{\\quad}6.5$$", "steps": [ { "type": "definition", "title": "Median", "text": "The median is the value separating the higher half of the data set, from the lower half.<br/>If the number of terms is odd, then the median is the middle element of the sorted set<br/>If the number of terms is even, then the median is the arithmetic mean of the two middle elements of the sorted set" }, { "type": "step", "primary": "Arrange the terms in ascending order", "result": "3,\\:3,\\:3,\\:4,\\:6,\\:7,\\:7,\\:7,\\:8,\\:10" }, { "type": "interim", "title": "Find the median of the ascending set:$${\\quad}6.5$$", "steps": [ { "type": "step", "primary": "Count the number of terms in the data set", "result": "\\begin{Bmatrix}3&3&3&4&6&7&7&7&8&10\\\\1&2&3&4&5&6&7&8&9&10\\end{Bmatrix}" }, { "type": "step", "primary": "The number of terms in the data set is", "result": "10" }, { "type": "step", "primary": "Since the number of terms is even, the median is the average of the two middle elements: $$6,\\:7$$" }, { "type": "interim", "title": "Arithmetic Mean (average) of $$6,\\:7:{\\quad}6.5$$", "steps": [ { "type": "definition", "title": "Arithmetic Mean", "text": "The arithemtic mean (average) is the sum of the values in the set divided by the number of elements in that set.<br/>If our data set contains the values $$a_{1},\\:\\ldots\\:,\\:a_{n}$$ (n elements) then the average$$=\\frac{1}{n}\\sum_{i=1}^{n}a_{i}\\:$$" }, { "type": "interim", "title": "Compute the sum of the data set:$${\\quad}\\sum_{i=1}^{n}a_{i}=13$$", "steps": [ { "type": "step", "primary": "Take the sum of $$6,\\:7$$", "result": "6+7" }, { "type": "step", "primary": "Simplify", "result": "13" } ], "meta": { "interimType": "Take Sum Of Set Title 0Eq" } }, { "type": "interim", "title": "Compute the number of terms in the data set:$${\\quad}n=2$$", "input": "6,\\:7", "steps": [ { "type": "step", "primary": "Count the number of terms in the data set", "result": "\\begin{Bmatrix}6&7\\\\1&2\\end{Bmatrix}" }, { "type": "step", "primary": "The number of terms in the data set is", "result": "2" } ], "meta": { "interimType": "Compute Number Terms Specific 0Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3K5O+fXcZudMI+14ZU5ZwQp9wy31HdDJRMD4uiaWz07swGDq7iA6052JsaffwjYCAdiL2sm5uEOurvfQtZ4ZYm72wZm7kDUxdE6YSmfEbr2nwpzh0cqJple1Qg84Yie2TwMdRtx07SOjqpi8nxLqBr55m6bbRWPxQuLu/BzFPGZ4mpXFf3SOUx+H18qfp3MLg=" } }, { "type": "interim", "title": "Divide the sum by the number of terms and simplify:$${\\quad}6.5$$", "steps": [ { "type": "step", "primary": "Divide the sum by the number of terms:$${\\quad}\\frac{\\sum_{i=1}^{n}a_{i}}{n}=\\frac{13}{2}$$", "result": "\\frac{13}{2}" }, { "type": "step", "primary": "Simplify", "result": "6.5" } ], "meta": { "interimType": "Compute The Average Title 0Eq" } }, { "type": "step", "result": "=6.5" } ], "meta": { "interimType": "Arithmetic Mean Top 1Eq" } }, { "type": "step", "result": "6.5" } ], "meta": { "interimType": "Get Median From Ascending List 0Eq" } }, { "type": "step", "result": "6.5" } ] } }