We study standard deviation. In statistics, we have learned using mean to find the average, and we have learned to use range to see the spread of the data. But range is not very good as the tool to represent the spread of the data.<\/p>\n\n\n\n
A better way is the measure called standard deviation:<\/p>\n\n\n\n
Standard Deviation SD = sqrt(sum of (Xi \u2013 AvgX)^2\/N)<\/p>\n\n\n\n
where N is the total number of data, AvgX is the mean of the data. Xi \u2013 AvgX is called the deviation of Xi from the mean AvgX for each i = 1, 2, \u2026, N<\/p>\n\n\n\n
[Sorry, I can\u2019t type using the summation notation sigma, which is what we learn in the class. This will simplify the writing.]<\/p>\n\n\n\n
Here is a written proof <\/a>of going from the definition to a formulae often used:<\/p>\n\n\n\n sqrt(\u2211(Xi \u2013 AvgX)^2 \/ N) = \u2211Xi^2 \/ N \u2013 (\u2211Xi \/ N)^2<\/p>\n\n\n\n I showed the proof in the classroom, but students may not get it.<\/p>\n\n\n\n Homework (pages are links, click to download):<\/p>\n\n\n\n Page 1<\/a>\u00a0 and\u00a0Page 2<\/a>: #1, #4, #5, #6.<\/p>\n","protected":false},"excerpt":{"rendered":" We study standard deviation. In statistics, we have learned using mean to find the average, and we have learned to use range to see the spread of the data. But range is not very good as the tool to represent the spread of the data. A better way is the measure called standard deviation: Standard […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0},"categories":[30,4,20,3],"tags":[],"_links":{"self":[{"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/posts\/1710"}],"collection":[{"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/comments?post=1710"}],"version-history":[{"count":1,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/posts\/1710\/revisions"}],"predecessor-version":[{"id":1711,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/posts\/1710\/revisions\/1711"}],"wp:attachment":[{"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/media?parent=1710"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/categories?post=1710"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/tags?post=1710"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}