{"id":435,"date":"2022-07-11T17:34:37","date_gmt":"2022-07-11T17:34:37","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/alphamodule\/?post_type=chapter&p=435"},"modified":"2022-07-11T17:40:35","modified_gmt":"2022-07-11T17:40:35","slug":"calculating-the-mean-and-median-of-a-data-set-learn-it-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/calculating-the-mean-and-median-of-a-data-set-learn-it-2\/","title":{"raw":"Calculating the Mean and Median of a Data Set: Learn It 2","rendered":"Calculating the Mean and Median of a Data Set: Learn It 2"},"content":{"raw":"

Median<\/h2>\r\nAnother measure of center you may recall is the median<\/strong>. This value is computed by ordering the data values and identifying the value in \u201cthe middle.\u201d\r\n\r\nIf we consider the sample data from above, ordering these values from least to greatest, we get:\r\n

[latex]1.2\\qquad 3.3\\qquad 3.6\\qquad 4.5\\qquad 5.8\\qquad 8.7\\qquad 10.0[\/latex]<\/p>\r\nThe value\u00a0[latex]4.5[\/latex] is the \u201cmiddle number\u201d in the ordered set; we see there are three values less than\u00a0[latex]4.5[\/latex] ([latex]1.2, 3.3, 3.6[\/latex]) and three values greater than\u00a0[latex]4.5[\/latex] ([latex]5.8, 8.7, 10.0[\/latex]). The value [latex]4.5[\/latex] is the median.\r\n

[latex]\\cancel{1.2}\\qquad \\cancel{3.3}\\qquad \\cancel{3.6}\\qquad 4.5\\qquad \\cancel{5.8}\\qquad \\cancel{8.7}\\qquad \\cancel{10.0}[\/latex]<\/p>\r\nIf there are an odd number of observations, the \"middle number\" is the number that is left alone after all of the others have been crossed out. If there are an even number of observations, the \u201cmiddle number\u201d is the mean of the middle two observations. Check out the following videos to practice finding the median. The first video is using an odd number of observations, and the second is using an even number of observations.\r\n

\r\n

finding the median using an odd numbered data set<\/h3>\r\nNeed a video demo showing the \"counting in from the ends\" to find the middle-most number in an odd numbered set.-->video starts at 2:00, it should stop around 2:48.\u00a0<\/span>\r\n\r\n[embed]https:\/\/youtu.be\/A1mQ9kD-i9I?t=120[\/embed]\r\n\r\n<\/div>\r\n
\r\n

finding the median using an even numbered data set<\/h3>\r\nNeed a video demo showing the \"counting in from the ends\" to find the middle-most number in an even numbered set.-->same video but starting at 10:32 and it should stop around 11:22.<\/span>\r\n\r\n[embed]https:\/\/youtu.be\/A1mQ9kD-i9I?t=632[\/embed]\r\n\r\n<\/div>\r\n
\r\n

Examples<\/h3>\r\nCalculate the median of each small data set below. These are the same sets used earlier to calculate the mean.\r\n

a)\u00a0[latex]7, 4, 8, 2, 3, 6[\/latex]<\/p>\r\n

b)\u00a0[latex]1.2, 3.9, 5.3, 4.2[\/latex]<\/p>\r\n

c)\u00a0[latex]79, 86, 92, 93, 88[\/latex]<\/p>\r\n[reveal-answer q=\"296010\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"296010\"]\r\n\r\na)\u00a0 \u00a0The median is\u00a0[latex]5[\/latex].\r\n

Put the numbers in order:\u00a0[latex]2, 3, 4, 6, 7, 8[\/latex]. Since there are an even number of values in the set, identify and take the average of the middle two: [latex]\\cancel{2}[\/latex], [latex]\\cancel{3}[\/latex], 4, 6, [latex]\\cancel{7}[\/latex], [latex]\\cancel{8}[\/latex]. The two numbers in the center spot are\u00a0[latex]4[\/latex] and\u00a0[latex]6[\/latex].\u00a0 [latex]\\frac{4+6}{2}=5[\/latex].<\/p>\r\nb)\u00a0 The median is\u00a0[latex]4.05[\/latex].\r\n

Put the numbers in order:\u00a0[latex]1.2, 3.9, 4.2, 5.3[\/latex]. Since there are an even number of values in the set, identify and take the average of the middle two:\u00a0[latex]\\cancel{1.2}\\text{, }[\/latex]3.9, 4.2, [latex]\\cancel{5.3}\\text{, }[\/latex]. The two numbers in the center spot are\u00a0[latex]3.9[\/latex] and\u00a0[latex]4.2[\/latex]. [latex]\\frac{3.9+4.2}{2}=4.05[\/latex].<\/p>\r\nc)\u00a0 The median is\u00a0[latex]88[\/latex].\r\n

Put the numbers in order:\u00a0[latex]79, 86, 88, 92, 93[\/latex]. Since there are an odd number of values in the set, identify and take the middle number as the median: [latex]\\cancel{79}\\text{, } \\cancel{86}\\text{, } 88\\text{, } \\cancel{92}\\text{, }\\cancel{93}[\/latex]. The middle number is\u00a0[latex]88[\/latex].<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNow you try it by taking the mean and median of the small set of data below.\r\n

\r\n

question 1<\/h3>\r\n[ohm_question hide_question_numbers=1]240965[\/ohm_question]\r\n\r\n[reveal-answer q=\"125513\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"125513\"]Recall that the median is the mean of the middle two values.[\/hidden-answer]\r\n\r\n<\/div>","rendered":"

Median<\/h2>\n

Another measure of center you may recall is the median<\/strong>. This value is computed by ordering the data values and identifying the value in \u201cthe middle.\u201d<\/p>\n

If we consider the sample data from above, ordering these values from least to greatest, we get:<\/p>\n

[latex]1.2\\qquad 3.3\\qquad 3.6\\qquad 4.5\\qquad 5.8\\qquad 8.7\\qquad 10.0[\/latex]<\/p>\n

The value\u00a0[latex]4.5[\/latex] is the \u201cmiddle number\u201d in the ordered set; we see there are three values less than\u00a0[latex]4.5[\/latex] ([latex]1.2, 3.3, 3.6[\/latex]) and three values greater than\u00a0[latex]4.5[\/latex] ([latex]5.8, 8.7, 10.0[\/latex]). The value [latex]4.5[\/latex] is the median.<\/p>\n

[latex]\\cancel{1.2}\\qquad \\cancel{3.3}\\qquad \\cancel{3.6}\\qquad 4.5\\qquad \\cancel{5.8}\\qquad \\cancel{8.7}\\qquad \\cancel{10.0}[\/latex]<\/p>\n

If there are an odd number of observations, the “middle number” is the number that is left alone after all of the others have been crossed out. If there are an even number of observations, the \u201cmiddle number\u201d is the mean of the middle two observations. Check out the following videos to practice finding the median. The first video is using an odd number of observations, and the second is using an even number of observations.<\/p>\n

\n

finding the median using an odd numbered data set<\/h3>\n

Need a video demo showing the “counting in from the ends” to find the middle-most number in an odd numbered set.–>video starts at 2:00, it should stop around 2:48.\u00a0<\/span><\/p>\n