arithmeticmean of 2,4,4,5,6,6,7,8,12

{ "query": { "display": "average $$2,\\:4,\\:4,\\:5,\\:6,\\:6,\\:7,\\:8,\\:12$$", "symbolab_question": "STATISTICS#arithmeticmean 2,4,4,5,6,6,7,8,12" }, "solution": { "level": "PERFORMED", "subject": "Statistics", "topic": "arithmeticmean", "subTopic": "Other", "default": "6" }, "steps": { "type": "interim", "title": "Arithmetic Mean (average) of $$2,\\:4,\\:4,\\:5,\\:6,\\:6,\\:7,\\:8,\\:12:{\\quad}6$$", "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:$${\\quad}\\sum_{i=1}^{n}a_{i}=54$$", "steps": [ { "type": "step", "primary": "Take the sum of $$2,\\:4,\\:4,\\:5,\\:6,\\:6,\\:7,\\:8,\\:12$$", "result": "2+4+4+5+6+6+7+8+12" }, { "type": "step", "primary": "Simplify", "result": "54" } ], "meta": { "interimType": "Take Sum Of Set Title 0Eq" } }, { "type": "interim", "title": "Compute the number of terms in the data set:$${\\quad}n=9$$", "input": "2,\\:4,\\:4,\\:5,\\:6,\\:6,\\:7,\\:8,\\:12", "steps": [ { "type": "step", "primary": "Count the number of terms in the data set", "result": "\\begin{Bmatrix}2&4&4&5&6&6&7&8&12\\\\1&2&3&4&5&6&7&8&9\\end{Bmatrix}" }, { "type": "step", "primary": "The number of terms in the data set is", "result": "9" } ], "meta": { "interimType": "Compute Number Terms Specific 0Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3K5O+fXcZudMI+14ZU5ZwQp9wy31HdDJRMD4uiaWz07swGDq7iA6052JsaffwjYCBMwz5bj4eAGccbyVkXotCzNcLJh3xr3BssPn0NSNFgE4EFMST8lDZxn1Yq5HMKVTuBfctShSHh6o1KVeK66PNwqHlHmj2LEZNQA+tirpyA3vsgXRauuNBTJjmQEDk/XzCwiNrEngO+NNvZ9sqNu+2V" } }, { "type": "interim", "title": "Divide the sum by the number of terms and simplify:$${\\quad}6$$", "steps": [ { "type": "step", "primary": "Divide the sum by the number of terms:$${\\quad}\\frac{\\sum_{i=1}^{n}a_{i}}{n}=\\frac{54}{9}$$", "result": "\\frac{54}{9}" }, { "type": "step", "primary": "Simplify", "result": "6" } ], "meta": { "interimType": "Compute The Average Title 0Eq" } }, { "type": "step", "result": "=6" } ] } }