{"id":4599,"date":"2015-05-11T01:30:01","date_gmt":"2015-05-11T06:30:01","guid":{"rendered":"http:\/\/www.thejuliagroup.com\/blog\/?p=4599"},"modified":"2015-05-11T01:32:17","modified_gmt":"2015-05-11T06:32:17","slug":"probability-and-z-scores","status":"publish","type":"post","link":"https:\/\/www.thejuliagroup.com\/blog\/probability-and-z-scores\/","title":{"rendered":"Probability and z-scores"},"content":{"rendered":"

For many students just learning statistics, the relationship of z-scores and probability is confusing.<\/p>\n

Let’s try this concrete example. Here is a chart of the distribution of height in a sample of over\u00a02,800 women.<\/p>\n

\"distribution<\/a><\/p>\n

 <\/p>\n

Notice that the peak, the mode is around 62-63\u00a0inches.<\/p>\n

You can see the frequency table here, as well as a larger picture of the histogram. <\/a>You’ll notice the median is between\u00a062 and 63 inches<\/p>\n

The mean is 62.7 – between 62 and 63 inches.<\/p>\n

Looks like a normal distribution in that mean = median = mode.<\/p>\n

Let’s go back to that mean of 62.7 inches. The standard deviation in this population is 2.46. \u00a0 What would 2 standard deviations above the mean be? Let’s round our 2 x 2.46 = 4.92 up to 5.<\/p>\n

The mean + 2 standard deviations = 62.7 + 5 = 67.7<\/p>\n

\"height<\/a><\/p>\n

If you look at the frequency distribution you’ll see that 97.3% of the people measured had a height of 67 inches or less<\/a>.<\/p>\n

So, this is a perfect demonstration of what we mean when we say that 97.5% of the people fall below 2 standard deviations above the mean.<\/p>\n","protected":false},"excerpt":{"rendered":"

For many students just learning statistics, the relationship of z-scores and probability is confusing. Let’s try this concrete example. Here is a chart of the distribution of height in a sample of over\u00a02,800 women.   Notice that the peak, the mode is around 62-63\u00a0inches. You can see the frequency table here, as well as a…<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_kad_post_classname":"","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[11],"tags":[],"class_list":["post-4599","post","type-post","status-publish","format-standard","hentry","category-statistics"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/posts\/4599","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/comments?post=4599"}],"version-history":[{"count":3,"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/posts\/4599\/revisions"}],"predecessor-version":[{"id":4605,"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/posts\/4599\/revisions\/4605"}],"wp:attachment":[{"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/media?parent=4599"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/categories?post=4599"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/tags?post=4599"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}