{"id":1622,"date":"2019-10-06T16:29:41","date_gmt":"2019-10-06T20:29:41","guid":{"rendered":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/?p=1622"},"modified":"2019-10-02T21:17:38","modified_gmt":"2019-10-03T01:17:38","slug":"math-9-lesson-5-fall-2019-1062019","status":"publish","type":"post","link":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/2019\/10\/06\/math-9-lesson-5-fall-2019-1062019\/","title":{"rendered":"Math 9, Lesson 5, Fall 2019, 10\/6\/2019"},"content":{"rendered":"
\n

We study standard deviation. In statistics, we have learned using mean to find the average, and we have learned to use range and interquartile range to see the spread of the data. But both range and interquartile range are not very good as the tool to represent the spread of the data.<\/p>\n

A better way is the measure called standard deviation:<\/p>\n

Standard Deviation SD = sqrt(sum of (Xi \u2013 AvgX)^2\/N)<\/p>\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

For a set of grouped data in the form of a frequency table, we have<\/p>\n

Mean AvgX = sum of fx \/ sum of f<\/p>\n

where x is the class mark of each class and f is the frequency of the corresponding class.<\/p>\n

Standard Deviation SD = sqrt(sum of f(Xi \u2013 AvgX)^2 \/ sum of f)<\/p>\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

Here is a\u00a0written proof\u00a0<\/a>of going from the definition to a formulae often used:<\/p>\n

sqrt(\u2211(Xi \u2013 AvgX)^2 \/ N) = \u2211Xi^2 \/ N \u2013 (\u2211Xi \/ N)^2<\/p>\n

I showed the proof in the classroom, but students may not get it.<\/p>\n

Homework (pages are links, click to download):<\/p>\n

Page 1<\/a>\u00a0 and\u00a0Page 2<\/a>: #1, #2, #3, #4, #5, #6.<\/p>\n<\/div>\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 and interquartile range to see the spread of the data. But both range and interquartile range are not very good as the tool to represent the spread of the data. A better way […]<\/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":[28,4,20,3],"tags":[],"_links":{"self":[{"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/posts\/1622"}],"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=1622"}],"version-history":[{"count":1,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/posts\/1622\/revisions"}],"predecessor-version":[{"id":1623,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/posts\/1622\/revisions\/1623"}],"wp:attachment":[{"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/media?parent=1622"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/categories?post=1622"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/tags?post=1622"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}