geometricmean of 8,6,6,5,8

{ "query": { "display": "geometric mean $$8,\\:6,\\:6,\\:5,\\:8$$", "symbolab_question": "STATISTICS#geometricmean 8,6,6,5,8" }, "solution": { "level": "PERFORMED", "subject": "Statistics", "topic": "geometricmean", "subTopic": "Other", "default": "6.49068…" }, "steps": { "type": "interim", "title": "Geometric Mean of $$8,\\:6,\\:6,\\:5,\\:8:{\\quad}6.49068…$$", "steps": [ { "type": "definition", "title": "Geometric Mean", "text": "For a data set with $$n$$ terms, the geometric mean is nth root of the product of the values in that set.<br/>If our data set contains the values $$a_{1},\\:\\ldots\\:,\\:a_{n}$$ (n elements) then the geometric mean$$=\\sqrt[n]{a_{1}\\cdot{a_{2}}\\cdots{a_{n}}}\\:$$" }, { "type": "interim", "title": "Compute the product of the data set:$${\\quad}a_{1}\\cdot{a_{2}}\\cdots{a_{n}}=11520$$", "steps": [ { "type": "step", "primary": "Take the product of $$8,\\:6,\\:6,\\:5,\\:8$$", "result": "8\\cdot\\:6\\cdot\\:6\\cdot\\:5\\cdot\\:8" }, { "type": "step", "primary": "Simplify", "result": "11520" } ], "meta": { "interimType": "Take Product Of Set Title 0Eq" } }, { "type": "interim", "title": "Compute the number of terms in the data set:$${\\quad}n=5$$", "input": "8,\\:6,\\:6,\\:5,\\:8", "steps": [ { "type": "step", "primary": "Count the number of terms in the data set", "result": "\\begin{Bmatrix}8&6&6&5&8\\\\1&2&3&4&5\\end{Bmatrix}" }, { "type": "step", "primary": "The number of terms in the data set is", "result": "5" } ], "meta": { "interimType": "Compute Number Terms Specific 0Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3K5O+fXcZudMI+14ZU5ZwQp9wy31HdDJRMD4uiaWz07swGDq7iA6052JsaffwjYCDAIlQ7EpI9I9Ds/VgQuV56qTfqO5p3n1xPuuHORLItyZtZ2LzqutQtdoMCJ6918WciT602TnmSVepWoa7xdEhGOhO9rEjQ+VKJ5P/GQjsW0vCOZuGwwTAbIcbqxu8Vqok=" } }, { "type": "interim", "title": "Compute $$\\sqrt[n]{a_{1}\\cdot{a_{2}}\\cdots{a_{n}}}:{\\quad}6.49068…$$", "steps": [ { "type": "step", "primary": "$$\\sqrt[n]{a_{1}\\cdot{a_{2}}\\cdots{a_{n}}}=\\sqrt[5]{11520}$$", "result": "\\sqrt[5]{11520}" }, { "type": "step", "primary": "Simplify", "result": "6.49068…" } ], "meta": { "interimType": "Compute The Geometric Mean Title 0Eq" } }, { "type": "step", "result": "=6.49068…" } ] } }