arithmeticmean of 6,7,8,12

{ "query": { "display": "average $$6,\\:7,\\:8,\\:12$$", "symbolab_question": "STATISTICS#arithmeticmean 6,7,8,12" }, "solution": { "level": "PERFORMED", "subject": "Statistics", "topic": "arithmeticmean", "subTopic": "Other", "default": "8.25" }, "steps": { "type": "interim", "title": "Arithmetic Mean (average) of $$6,\\:7,\\:8,\\:12:{\\quad}8.25$$", "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:$${\\quad}\\sum_{i=1}^{n}a_{i}=33$$", "steps": [ { "type": "step", "primary": "Take the sum of $$6,\\:7,\\:8,\\:12$$", "result": "6+7+8+12" }, { "type": "step", "primary": "Simplify", "result": "33" } ], "meta": { "interimType": "Take Sum Of Set Title 0Eq" } }, { "type": "interim", "title": "Compute the number of terms in the data set:$${\\quad}n=4$$", "input": "6,\\:7,\\:8,\\:12", "steps": [ { "type": "step", "primary": "Count the number of terms in the data set", "result": "\\begin{Bmatrix}6&7&8&12\\\\1&2&3&4\\end{Bmatrix}" }, { "type": "step", "primary": "The number of terms in the data set is", "result": "4" } ], "meta": { "interimType": "Compute Number Terms Specific 0Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3K5O+fXcZudMI+14ZU5ZwQp9wy31HdDJRMD4uiaWz07swGDq7iA6052JsaffwjYCDfPIDLM68CnM+mFOV6VZue5g5ol4Ple/TlcQ5gQvzs1VP7XdP66vn2lDIgOgst4mQ9fU0gki1F3kpeiGX7zPpUTnSqtrWGjkBt21HjiWIXX2OP+J30Cgf6WYt1a2LENJA=" } }, { "type": "interim", "title": "Divide the sum by the number of terms and simplify:$${\\quad}8.25$$", "steps": [ { "type": "step", "primary": "Divide the sum by the number of terms:$${\\quad}\\frac{\\sum_{i=1}^{n}a_{i}}{n}=\\frac{33}{4}$$", "result": "\\frac{33}{4}" }, { "type": "step", "primary": "Simplify", "result": "8.25" } ], "meta": { "interimType": "Compute The Average Title 0Eq" } }, { "type": "step", "result": "=8.25" } ] } }