arithmeticmean of 2,2,1,3,1,3,1,2,3,2,4,2,2,1

{ "query": { "display": "average $$2,\\:2,\\:1,\\:3,\\:1,\\:3,\\:1,\\:2,\\:3,\\:2,\\:4,\\:2,\\:2,\\:1$$", "symbolab_question": "STATISTICS#arithmeticmean 2,2,1,3,1,3,1,2,3,2,4,2,2,1" }, "solution": { "level": "PERFORMED", "subject": "Statistics", "topic": "arithmeticmean", "subTopic": "Other", "default": "2.07142…" }, "steps": { "type": "interim", "title": "Arithmetic Mean (average) of $$2,\\:2,\\:1,\\:3,\\:1,\\:3,\\:1,\\:2,\\:3,\\:2,\\:4,\\:2,\\:2,\\:1:{\\quad}2.07142…$$", "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:$${\\quad}\\sum_{i=1}^{n}a_{i}=29$$", "steps": [ { "type": "step", "primary": "Take the sum of $$2,\\:2,\\:1,\\:3,\\:1,\\:3,\\:1,\\:2,\\:3,\\:2,\\:4,\\:2,\\:2,\\:1$$", "result": "2+2+1+3+1+3+1+2+3+2+4+2+2+1" }, { "type": "step", "primary": "Simplify", "result": "29" } ], "meta": { "interimType": "Take Sum Of Set Title 0Eq" } }, { "type": "interim", "title": "Compute the number of terms in the data set:$${\\quad}n=14$$", "input": "2,\\:2,\\:1,\\:3,\\:1,\\:3,\\:1,\\:2,\\:3,\\:2,\\:4,\\:2,\\:2,\\:1", "steps": [ { "type": "step", "primary": "Count the number of terms in the data set", "result": "\\begin{Bmatrix}2&2&1&3&1&3&1&2&3&2&4&2&2&1\\\\1&2&3&4&5&6&7&8&9&10&11&12&13&14\\end{Bmatrix}" }, { "type": "step", "primary": "The number of terms in the data set is", "result": "14" } ], "meta": { "interimType": "Compute Number Terms Specific 0Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3K5O+fXcZudMI+14ZU5ZwQp9wy31HdDJRMD4uiaWz07swGDq7iA6052JsaffwjYCDsuwo1y/W3Yn8dtrvMrX8B/hNtSkgUH/+LSRIKzqYJg5VY+TzjZXTjQtozDJTk9lU4S5nd8Z8AmLMF7+7F3eT/6q0JhXK5yuKLlAPtjtIQNPNkg0IYzD43BdqCmsUyk8gs5jEkeEbGnbbcByfWqBQ5" } }, { "type": "interim", "title": "Divide the sum by the number of terms and simplify:$${\\quad}2.07142…$$", "steps": [ { "type": "step", "primary": "Divide the sum by the number of terms:$${\\quad}\\frac{\\sum_{i=1}^{n}a_{i}}{n}=\\frac{29}{14}$$", "result": "\\frac{29}{14}" }, { "type": "step", "primary": "Simplify", "result": "2.07142…" } ], "meta": { "interimType": "Compute The Average Title 0Eq" } }, { "type": "step", "result": "=2.07142…" } ] } }