arithmeticmean of 1/10 ,9,8,7,8,6,10,6

{ "query": { "display": "average $$\\frac{1}{10},\\:9,\\:8,\\:7,\\:8,\\:6,\\:10,\\:6$$", "symbolab_question": "STATISTICS#arithmeticmean \\frac{1}{10},9,8,7,8,6,10,6" }, "solution": { "level": "PERFORMED", "subject": "Statistics", "topic": "arithmeticmean", "subTopic": "Other", "default": "6.7625" }, "steps": { "type": "interim", "title": "Arithmetic Mean (average) of $$\\frac{1}{10},\\:9,\\:8,\\:7,\\:8,\\:6,\\:10,\\:6:{\\quad}6.7625$$", "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:$${\\quad}\\sum_{i=1}^{n}a_{i}=54.1$$", "steps": [ { "type": "step", "primary": "Take the sum of $$\\frac{1}{10},\\:9,\\:8,\\:7,\\:8,\\:6,\\:10,\\:6$$", "result": "\\frac{1}{10}+9+8+7+8+6+10+6" }, { "type": "step", "primary": "Simplify", "result": "54.1" } ], "meta": { "interimType": "Take Sum Of Set Title 0Eq" } }, { "type": "interim", "title": "Compute the number of terms in the data set:$${\\quad}n=8$$", "input": "\\frac{1}{10},\\:9,\\:8,\\:7,\\:8,\\:6,\\:10,\\:6", "steps": [ { "type": "step", "primary": "Count the number of terms in the data set", "result": "\\begin{Bmatrix}\\frac{1}{10}&9&8&7&8&6&10&6\\\\1&2&3&4&5&6&7&8\\end{Bmatrix}" }, { "type": "step", "primary": "The number of terms in the data set is", "result": "8" } ], "meta": { "interimType": "Compute Number Terms Specific 0Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3K5O+fXcZudMI+14ZU5ZwQp9wy31HdDJRMD4uiaWz07swGDq7iA6052JsaffwjYCDXnI8tPahDmkV+ZESusPMktaZnMyaMf5gyT/9hMde5wIwI6VWtywTB+sIDMjMOVI6LifS/no/lKgUB6yosDJRjcdru9MMn3l9xuClr36vENRqKPVmAjIhZFFd8vBytJpD7Nqd2VVQW8BLy173gMCFt" } }, { "type": "interim", "title": "Divide the sum by the number of terms and simplify:$${\\quad}6.7625$$", "steps": [ { "type": "step", "primary": "Divide the sum by the number of terms:$${\\quad}\\frac{\\sum_{i=1}^{n}a_{i}}{n}=\\frac{54.1}{8}$$", "result": "\\frac{54.1}{8}" }, { "type": "step", "primary": "Simplify", "result": "6.7625" } ], "meta": { "interimType": "Compute The Average Title 0Eq" } }, { "type": "step", "result": "=6.7625" } ] } }