geometricmean of 10,18

{ "query": { "display": "geometric mean $$10,\\:18$$", "symbolab_question": "STATISTICS#geometricmean 10,18" }, "solution": { "level": "PERFORMED", "subject": "Statistics", "topic": "geometricmean", "subTopic": "Other", "default": "13.41640…" }, "steps": { "type": "interim", "title": "Geometric Mean of $$10,\\:18:{\\quad}13.41640…$$", "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:$${\\quad}a_{1}\\cdot{a_{2}}\\cdots{a_{n}}=180$$", "steps": [ { "type": "step", "primary": "Take the product of $$10,\\:18$$", "result": "10\\cdot\\:18" }, { "type": "step", "primary": "Simplify", "result": "180" } ], "meta": { "interimType": "Take Product Of Set Title 0Eq" } }, { "type": "interim", "title": "Compute the number of terms in the data set:$${\\quad}n=2$$", "input": "10,\\:18", "steps": [ { "type": "step", "primary": "Count the number of terms in the data set", "result": "\\begin{Bmatrix}10&18\\\\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+14ZU5ZwQp9wy31HdDJRMD4uiaWz07swGDq7iA6052JsaffwjYCA2ut3JUUjuO0t+KQocO4i7o3oe/oyhMy2+1TQhDBd2f50/f39vi/im7LgV11RvVe6/ziMkXXr+I47MORkfuCKRooq3uMWokbqNeRLYGE+SYj31Q4NZHkSR6jjJYmg7eTU=" } }, { "type": "interim", "title": "Compute $$\\sqrt[n]{a_{1}\\cdot{a_{2}}\\cdots{a_{n}}}:{\\quad}13.41640…$$", "steps": [ { "type": "step", "primary": "$$\\sqrt[n]{a_{1}\\cdot{a_{2}}\\cdots{a_{n}}}=\\sqrt{180}$$", "result": "\\sqrt{180}" }, { "type": "step", "primary": "Simplify", "result": "13.41640…" } ], "meta": { "interimType": "Compute The Geometric Mean Title 0Eq" } }, { "type": "step", "result": "=13.41640…" } ] } }