arithmeticmean of 65,68,69,70,71,72,90,95

{ "query": { "display": "average $$65,\\:68,\\:69,\\:70,\\:71,\\:72,\\:90,\\:95$$", "symbolab_question": "STATISTICS#arithmeticmean 65,68,69,70,71,72,90,95" }, "solution": { "level": "PERFORMED", "subject": "Statistics", "topic": "arithmeticmean", "subTopic": "Other", "default": "75" }, "steps": { "type": "interim", "title": "Arithmetic Mean (average) of $$65,\\:68,\\:69,\\:70,\\:71,\\:72,\\:90,\\:95:{\\quad}75$$", "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:$${\\quad}\\sum_{i=1}^{n}a_{i}=600$$", "steps": [ { "type": "step", "primary": "Take the sum of $$65,\\:68,\\:69,\\:70,\\:71,\\:72,\\:90,\\:95$$", "result": "65+68+69+70+71+72+90+95" }, { "type": "step", "primary": "Simplify", "result": "600" } ], "meta": { "interimType": "Take Sum Of Set Title 0Eq" } }, { "type": "interim", "title": "Compute the number of terms in the data set:$${\\quad}n=8$$", "input": "65,\\:68,\\:69,\\:70,\\:71,\\:72,\\:90,\\:95", "steps": [ { "type": "step", "primary": "Count the number of terms in the data set", "result": "\\begin{Bmatrix}65&68&69&70&71&72&90&95\\\\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+14ZU5ZwQp9wy31HdDJRMD4uiaWz07swGDq7iA6052JsaffwjYCA3vmLIAVHf0LagtQrOD8mO74jEhiZzEUVo/7KnMC9OJT/L0MoYg+CUn6oyL3EO7YrN8mAvHZ+D0EKLtWnxurV5jSjY2PfmXG250CeNFWSQpmvO2EfSmoreSai299kP7ASHXuGidz+nNtDoeMyOIiZS" } }, { "type": "interim", "title": "Divide the sum by the number of terms and simplify:$${\\quad}75$$", "steps": [ { "type": "step", "primary": "Divide the sum by the number of terms:$${\\quad}\\frac{\\sum_{i=1}^{n}a_{i}}{n}=\\frac{600}{8}$$", "result": "\\frac{600}{8}" }, { "type": "step", "primary": "Simplify", "result": "75" } ], "meta": { "interimType": "Compute The Average Title 0Eq" } }, { "type": "step", "result": "=75" } ] } }