{"id":537,"date":"2022-07-15T17:57:29","date_gmt":"2022-07-15T17:57:29","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/alphamodule\/?post_type=chapter&p=537"},"modified":"2022-08-08T16:56:16","modified_gmt":"2022-08-08T16:56:16","slug":"interpreting-the-mean-and-median-of-a-data-set-dig-deeper","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/alphamodule\/chapter\/interpreting-the-mean-and-median-of-a-data-set-dig-deeper\/","title":{"raw":"Interpreting the Mean and Median of a Data Set: Dig Deeper","rendered":"Interpreting the Mean and Median of a Data Set: Dig Deeper"},"content":{"raw":"
\r\n

interactive example<\/h3>\r\nRecall that we think of the mean as the \"average\" data value and the median as the 50th percentile, the value that splits the data in half.\u00a0If needed, you may return to\u00a0Calculating the Mean and Median of a Data Set: What to Know<\/em><\/a> for a refresher of these interpretations of mean and median.\r\n\r\nExample: Let's say the mean of a data set is given as 10.5 and the median as 11. Which of the following statements are true? Explain.\r\n
    \r\n \t
  1. The median tells us a typical value for this data set. That is, if we took all the values and spread them evenly about, each value would be about 11.<\/li>\r\n \t
  2. About half the data values fall below 11 and half fall above.<\/li>\r\n \t
  3. The most common data value appearing is 10.5.<\/li>\r\n \t
  4. A typical data value for this set is 10.5. That is, if we distributed the sum of all the values evenly, each value would be about 10.5.<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"679737\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"679737\"]\r\n
      \r\n \t
    1. False. The median represents the 50th percentile, with about half the values falling above 11 and half below.<\/li>\r\n \t
    2. True. The median is 11.<\/li>\r\n \t
    3. The mode tells us the most common data value. Neither the mean nor the median gives us that information.<\/li>\r\n \t
    4. True. The mean is 10.5, which we can consider to be the \"average\" data value.<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>","rendered":"
      \n

      interactive example<\/h3>\n

      Recall that we think of the mean as the “average” data value and the median as the 50th percentile, the value that splits the data in half.\u00a0If needed, you may return to\u00a0Calculating the Mean and Median of a Data Set: What to Know<\/em><\/a> for a refresher of these interpretations of mean and median.<\/p>\n

      Example: Let’s say the mean of a data set is given as 10.5 and the median as 11. Which of the following statements are true? Explain.<\/p>\n

        \n
      1. The median tells us a typical value for this data set. That is, if we took all the values and spread them evenly about, each value would be about 11.<\/li>\n
      2. About half the data values fall below 11 and half fall above.<\/li>\n
      3. The most common data value appearing is 10.5.<\/li>\n
      4. A typical data value for this set is 10.5. That is, if we distributed the sum of all the values evenly, each value would be about 10.5.<\/li>\n<\/ol>\n
        Show Answer<\/span><\/p>\n
        \n
          \n
        1. False. The median represents the 50th percentile, with about half the values falling above 11 and half below.<\/li>\n
        2. True. The median is 11.<\/li>\n
        3. The mode tells us the most common data value. Neither the mean nor the median gives us that information.<\/li>\n
        4. True. The mean is 10.5, which we can consider to be the “average” data value.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":17533,"menu_order":38,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-537","chapter","type-chapter","status-publish","hentry"],"part":20,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/537","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/537\/revisions"}],"predecessor-version":[{"id":587,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/537\/revisions\/587"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/parts\/20"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapters\/537\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/media?parent=537"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/pressbooks\/v2\/chapter-type?post=537"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/contributor?post=537"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/alphamodule\/wp-json\/wp\/v2\/license?post=537"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}