arithmeticmean of 12.5,12.7,14.9,11.3,11.7,10.9

{ "query": { "display": "average $$12.5,\\:12.7,\\:14.9,\\:11.3,\\:11.7,\\:10.9$$", "symbolab_question": "STATISTICS#arithmeticmean 12.5,12.7,14.9,11.3,11.7,10.9" }, "solution": { "level": "PERFORMED", "subject": "Statistics", "topic": "arithmeticmean", "subTopic": "Other", "default": "12.33333…" }, "steps": { "type": "interim", "title": "Arithmetic Mean (average) of $$12.5,\\:12.7,\\:14.9,\\:11.3,\\:11.7,\\:10.9:{\\quad}12.33333…$$", "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:$${\\quad}\\sum_{i=1}^{n}a_{i}=74$$", "steps": [ { "type": "step", "primary": "Take the sum of $$12.5,\\:12.7,\\:14.9,\\:11.3,\\:11.7,\\:10.9$$", "result": "12.5+12.7+14.9+11.3+11.7+10.9" }, { "type": "step", "primary": "Simplify", "result": "74" } ], "meta": { "interimType": "Take Sum Of Set Title 0Eq" } }, { "type": "interim", "title": "Compute the number of terms in the data set:$${\\quad}n=6$$", "input": "12.5,\\:12.7,\\:14.9,\\:11.3,\\:11.7,\\:10.9", "steps": [ { "type": "step", "primary": "Count the number of terms in the data set", "result": "\\begin{Bmatrix}12.5&12.7&14.9&11.3&11.7&10.9\\\\1&2&3&4&5&6\\end{Bmatrix}" }, { "type": "step", "primary": "The number of terms in the data set is", "result": "6" } ], "meta": { "interimType": "Compute Number Terms Specific 0Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3K5O+fXcZudMI+14ZU5ZwQp9wy31HdDJRMD4uiaWz07swGDq7iA6052JsaffwjYCB2V+u3niuHB4X4kUqlMLqvBDEc9nIIyde6i22kwjMnGBI6cRhDCZax02coDo9ffyac0UAm97e3ZdFs70jM7AY+HtBxF4YoCq+yXnRYGozDl5B00w6UQ2s6IWYitDhNtoeji/kK9z21uZiIOjEhPZ+e" } }, { "type": "interim", "title": "Divide the sum by the number of terms and simplify:$${\\quad}12.33333…$$", "steps": [ { "type": "step", "primary": "Divide the sum by the number of terms:$${\\quad}\\frac{\\sum_{i=1}^{n}a_{i}}{n}=\\frac{74}{6}$$", "result": "\\frac{74}{6}" }, { "type": "step", "primary": "Simplify", "result": "12.33333…" } ], "meta": { "interimType": "Compute The Average Title 0Eq" } }, { "type": "step", "result": "=12.33333…" } ] } }