thirdquartile 9.4,48.4,35.4,37,29,31,64.4,37.4,16.6,28.6

{ "query": { "display": "upper quartile $$9.4,\\:48.4,\\:35.4,\\:37,\\:29,\\:31,\\:64.4,\\:37.4,\\:16.6,\\:28.6$$", "symbolab_question": "STATISTICS#thirdquartile 9.4,48.4,35.4,37,29,31,64.4,37.4,16.6,28.6" }, "solution": { "level": "PERFORMED", "subject": "Statistics", "topic": "thirdquartile", "subTopic": "Other", "default": "37.4" }, "steps": { "type": "interim", "title": "Third Quartile (upper quartile) of $$9.4,\\:48.4,\\:35.4,\\:37,\\:29,\\:31,\\:64.4,\\:37.4,\\:16.6,\\:28.6:{\\quad}37.4$$", "steps": [ { "type": "definition", "title": "Third Quartile", "text": "The third quartile is the value separating the lower three-quarters and higher quarters of the data set.<br/>The third quartile is computed by taking the median of the higher half of a sorted set." }, { "type": "step", "primary": "Arrange the terms in ascending order", "result": "9.4,\\:16.6,\\:28.6,\\:29,\\:31,\\:35.4,\\:37,\\:37.4,\\:48.4,\\:64.4" }, { "type": "interim", "title": "Take the upper half of the ascending set:$${\\quad}35.4,\\:37,\\:37.4,\\:48.4,\\:64.4$$", "steps": [ { "type": "step", "primary": "Count the number of terms in the data set", "result": "\\begin{Bmatrix}9.4&16.6&28.6&29&31&35.4&37&37.4&48.4&64.4\\\\1&2&3&4&5&6&7&8&9&10\\end{Bmatrix}" }, { "type": "step", "primary": "The number of terms in the data set is", "result": "10" }, { "type": "step", "primary": "Take the upper $$5$$ terms", "result": "35.4,\\:37,\\:37.4,\\:48.4,\\:64.4" } ], "meta": { "interimType": "Take The Upper Half Specific 0Eq" } }, { "type": "interim", "title": "Median of $$35.4,\\:37,\\:37.4,\\:48.4,\\:64.4:{\\quad}37.4$$", "steps": [ { "type": "definition", "title": "Median", "text": "The median is the value separating the higher half of the data set, from the lower half.<br/>If the number of terms is odd, then the median is the middle element of the sorted set<br/>If the number of terms is even, then the median is the arithmetic mean of the two middle elements of the sorted set" }, { "type": "step", "primary": "Arrange the terms in ascending order", "result": "35.4,\\:37,\\:37.4,\\:48.4,\\:64.4" }, { "type": "interim", "title": "Find the median of the ascending set:$${\\quad}37.4$$", "steps": [ { "type": "step", "primary": "Count the number of terms in the data set", "result": "\\begin{Bmatrix}35.4&37&37.4&48.4&64.4\\\\1&2&3&4&5\\end{Bmatrix}" }, { "type": "step", "primary": "The number of terms in the data set is", "result": "5" }, { "type": "step", "primary": "Since the number of terms is odd, the median is the middle element of the sorted set.", "result": "37.4" } ], "meta": { "interimType": "Get Median From Ascending List 0Eq" } }, { "type": "step", "result": "37.4" } ], "meta": { "interimType": "Median Top 1Eq" } }, { "type": "step", "result": "37.4" } ] } }