{"id":437,"date":"2022-07-11T17:34:42","date_gmt":"2022-07-11T17:34:42","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/alphamodule\/?post_type=chapter&p=437"},"modified":"2022-07-11T17:40:43","modified_gmt":"2022-07-11T17:40:43","slug":"calculating-the-mean-and-median-of-a-data-set-learn-it-4","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/calculating-the-mean-and-median-of-a-data-set-learn-it-4\/","title":{"raw":"Calculating the Mean and Median of a Data Set: Learn It 4","rendered":"Calculating the Mean and Median of a Data Set: Learn It 4"},"content":{"raw":"

Mean and Median as the Center of Data<\/h2>\r\nThere are other ways that we can think about the mean and median as measures of center of numerical data. More specifically, the mean represents the balance point of the data, and the median represents the\u00a0[latex]50[\/latex]th<\/sup> percentile, or the value that splits the data in half (i.e., half of the data are below the median and the other half of the data are above the median).\r\n
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mean and median<\/h3>\r\n[Perspective Video - a 3-instructor video illustrating the mean as a balance point and the median as splitting the data in half]<\/span>\r\n\r\n<\/div>\r\n
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question 3<\/h3>\r\n[ohm_question hide_question_numbers=1]240620[\/ohm_question]\r\n\r\n[reveal-answer q=\"509633\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"509633\"]Which choice would keep the histogram balanced if the x-axis was a scale and the heights of the columns were weights? It may be helpful to first eliminate the choices that clearly do not represent the balance point of the data.[\/hidden-answer]\r\n\r\n<\/div>\r\n
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question 4<\/h3>\r\n[ohm_question hide_question_numbers=1]240623[\/ohm_question]\r\n\r\n[reveal-answer q=\"694612\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"694612\"]The median will separate the data into equal halves: half of the data will be below the median and half will be above the median. It may be helpful to first eliminate the choices that clearly do not separate the data in half.[\/hidden-answer]\r\n\r\n<\/div>\r\n
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Using Technology to Calculate and Compare Centers Across Groups<\/h3>\r\n[Worked example video - a 3-instructor video providing an example like the one below for questions 5 - 7]<\/span>\r\n\r\n<\/div>\r\nAnother benefit of using technology to calculate the mean and median is that we can quickly calculate these values for multiple groups. We can do so by using the Several Groups<\/strong> tab on the\u00a0Describing and Exploring Quantitative Variables<\/em> tool (the same tool you used to complete questions 2 - 4 above).\r\n
\r\n\r\nGo to the Describing and Exploring Quantitative Variables<\/em> tool at https:\/\/dcmathpathways.shinyapps.io\/EDA_quantitative\/<\/a>.\r\n

Step 1) Select the Several Groups<\/strong> tab.<\/p>\r\n

Step 2) Under\u00a0Enter Data<\/strong>, select\u00a0From Textbook<\/strong>.<\/p>\r\n

Step 3) Locate the drop-down menu under Data Set<\/strong>, and select Sleep Study: Average Sleep Score<\/strong>.<\/p>\r\n

Step 4) Change Choose Type of Plot<\/strong>\u00a0to Histogram<\/strong> if desired.<\/p>\r\n

Step 5) Calculate the mean and median for each of the groups: \u201cOwl,\u201d \u201cLark,\u201d and \u201cNeither,\u201d and list these values in the table in question 5 below (Note: the mean and median will be automatically calculated by the technology and can be found under Descriptive Statistics).<\/p>\r\n\r\n<\/div>\r\nRecall that \u201cOwl\u201d describes the group of students who tends to stay up late, and \u201cLark\u201d describes the group who tends to wake up early. Students who did not identify as an owl nor a lark were classified in the \u201cNeither\u201d group.\r\n\r\nRecall also that we consider the mean to be the arithmetic mean (commonly called the\u00a0\"average\") of a set of numbers, while the median refers to the value that sits in the middle of the distribution with half of the values above it and half of the values below.\r\n

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question 5<\/h3>\r\n[ohm_question hide_question_numbers=1]240967[\/ohm_question]\r\n
\r\n\r\n[reveal-answer q=\"475952\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"475952\"]Locate these values in Descriptive Statistics in the tool. Confirm that you have Several Groups and data set Sleep Study: Average Sleep Score selected. The data in the tool may be presented in a different order than in this table.[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n
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question 6<\/h3>\r\n[ohm_question hide_question_numbers=1]240968[\/ohm_question]\r\n\r\n[reveal-answer q=\"832913\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"832913\"]The measure we commonly call an \"average\" is actually the mean of a data set. [\/hidden-answer]\r\n\r\n<\/div>\r\n
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question 7<\/h3>\r\n[ohm_question hide_question_numbers=1]240969[\/ohm_question]\r\n\r\n[reveal-answer q=\"863794\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"863794\"]Recall that the median for each group represents the\u00a0[latex]50^{\\text{th}}[\/latex]\u00a0percentile: half of the data values are below the median and half of the data values are above the median.[\/hidden-answer]\r\n\r\n<\/div>","rendered":"

Mean and Median as the Center of Data<\/h2>\n

There are other ways that we can think about the mean and median as measures of center of numerical data. More specifically, the mean represents the balance point of the data, and the median represents the\u00a0[latex]50[\/latex]th<\/sup> percentile, or the value that splits the data in half (i.e., half of the data are below the median and the other half of the data are above the median).<\/p>\n

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mean and median<\/h3>\n

[Perspective Video – a 3-instructor video illustrating the mean as a balance point and the median as splitting the data in half]<\/span><\/p>\n<\/div>\n

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question 3<\/h3>\n