firstquartile 8,9,11,5,10,13,4,7,9,13,12

{ "query": { "display": "lower quartile $$8,\\:9,\\:11,\\:5,\\:10,\\:13,\\:4,\\:7,\\:9,\\:13,\\:12$$", "symbolab_question": "STATISTICS#firstquartile 8,9,11,5,10,13,4,7,9,13,12" }, "solution": { "level": "PERFORMED", "subject": "Statistics", "topic": "firstquartile", "subTopic": "Other", "default": "7" }, "steps": { "type": "interim", "title": "First Quartile (lower quartile) of $$8,\\:9,\\:11,\\:5,\\:10,\\:13,\\:4,\\:7,\\:9,\\:13,\\:12:{\\quad}7$$", "steps": [ { "type": "definition", "title": "First Quartile", "text": "The first quartile is the value separating the lower quarter and higher three-quarters of the data set.<br/>The first quartile is computed by taking the median of the lower half of a sorted set." }, { "type": "step", "primary": "Arrange the terms in ascending order", "result": "4,\\:5,\\:7,\\:8,\\:9,\\:9,\\:10,\\:11,\\:12,\\:13,\\:13" }, { "type": "interim", "title": "Take the lower half of the ascending set:$${\\quad}4,\\:5,\\:7,\\:8,\\:9$$", "steps": [ { "type": "step", "primary": "Count the number of terms in the data set", "result": "\\begin{Bmatrix}4&5&7&8&9&9&10&11&12&13&13\\\\1&2&3&4&5&6&7&8&9&10&11\\end{Bmatrix}" }, { "type": "step", "primary": "The number of terms in the data set is", "result": "11" }, { "type": "step", "primary": "Since the number of terms is odd, take the elements below the middle one, that is, the lower $$5$$ elements$$.$$", "result": "4,\\:5,\\:7,\\:8,\\:9" } ], "meta": { "interimType": "Take The Lower Half Specific 0Eq" } }, { "type": "interim", "title": "Median of $$4,\\:5,\\:7,\\:8,\\:9:{\\quad}7$$", "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": "4,\\:5,\\:7,\\:8,\\:9" }, { "type": "interim", "title": "Find the median of the ascending set:$${\\quad}7$$", "steps": [ { "type": "step", "primary": "Count the number of terms in the data set", "result": "\\begin{Bmatrix}4&5&7&8&9\\\\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": "7" } ], "meta": { "interimType": "Get Median From Ascending List 0Eq" } }, { "type": "step", "result": "7" } ], "meta": { "interimType": "Median Top 1Eq" } }, { "type": "step", "result": "7" } ] } }