{"id":7001,"date":"2019-02-27T18:08:47","date_gmt":"2019-02-27T23:08:47","guid":{"rendered":"http:\/\/www.decisionsciencenews.com\/?p=7001"},"modified":"2019-07-29T00:41:01","modified_gmt":"2019-07-29T04:41:01","slug":"tips-for-drawing-a-normal-distribution","status":"publish","type":"post","link":"https:\/\/www.decisionsciencenews.com\/?p=7001","title":{"rendered":"Tips for drawing a normal distribution"},"content":{"rendered":"<p>KNOW THY INFLECTION POINT<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2019\/07\/snorm.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-7002\" src=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2019\/07\/snorm_s.png\" alt=\"\" width=\"454\" height=\"225\" srcset=\"https:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2019\/07\/snorm_s.png 454w, https:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2019\/07\/snorm_s-300x149.png 300w\" sizes=\"auto, (max-width: 454px) 100vw, 454px\" \/><\/a><br \/>\n<em>Click to Enlarge<\/em><\/p>\n<p>We have drawn a lot of sorry-looking normal distributions in our life. It&#8217;s a shape that&#8217;s hard to get down without a lot of practice.<\/p>\n<p>Here&#8217;s a few tips that can make it easier.<\/p>\n<ul>\n<li>Start by marking out standard deviations on the x axis from -3 to +3<\/li>\n<li>At x=0, draw a point to be the top of the bell curve<\/li>\n<li>At \u00b1 1 SDs draw points at about 5\/8ths of the height<\/li>\n<li>At \u00b1 2 SDs draw points at about 1\/8th of the height<\/li>\n<li>At \u00b1 3.25 SDs draw points on the X axis<\/li>\n<\/ul>\n<p>Now, to get the bends right, we exploit the following cool fact: There is an inflection point at \u00b11 standard deviation. That is,<\/p>\n<p><strong>At 1 standard deviation, the curve stops bending down and starts bending up. <\/strong><\/p>\n<p>Draw through those points and voila, normal distribution!<\/p>\n<p>You might be wondering if these tips are approximations or exact. The heights of the points are approximate but within 1-2% of the exact values. The inflection point at \u00b1 1 SD is real. That&#8217;s right, <a href=\"https:\/\/www.thoughtco.com\/inflection-points-of-a-normal-distribution-3126446\">the second derivative is 0 at exactly \u00b1 1 standard deviation<\/a>.<\/p>\n<p>RELATED BUT DIFFERENT DSN POST<br \/>\n<a href=\"http:\/\/www.decisionsciencenews.com\/2019\/03\/06\/how-to-eyeball-a-standard-deviation\/\">How to eyeball a standard deviation<\/a><\/p>\n<p>R CODE FOR THE PLOTS<br \/>\n<script src=\"https:\/\/gist.github.com\/dggoldst\/5dfdbf5b431509b35331ca287dd0a7f5.js\"><\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>KNOW THY INFLECTION POINT Click to Enlarge We have drawn a lot of sorry-looking normal distributions in our life. It&#8217;s a shape that&#8217;s hard to get down without a lot of practice. Here&#8217;s a few tips that can make it easier. Start by marking out standard deviations on the x axis from -3 to +3 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[4,74],"tags":[1838,1839,52,970,1138,1834,208,1833,1835,60,1691,1836,1208,59,1837,1399],"class_list":["post-7001","post","type-post","status-publish","format-standard","hentry","category-encyclopedia","category-r","tag-1-8th","tag-5-8ths","tag-decision","tag-deviation","tag-distribution","tag-draw","tag-goldstein","tag-how","tag-inflection","tag-news","tag-normal","tag-point","tag-r","tag-science","tag-sd","tag-standard"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4LKj-1OV","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/posts\/7001","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7001"}],"version-history":[{"count":8,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/posts\/7001\/revisions"}],"predecessor-version":[{"id":7019,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/posts\/7001\/revisions\/7019"}],"wp:attachment":[{"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7001"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7001"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7001"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}