{"id":2910,"date":"2011-07-05T14:57:11","date_gmt":"2011-07-05T12:57:11","guid":{"rendered":"https:\/\/ingmarverheij.com\/2011\/07\/average-mean-versus-median\/"},"modified":"2011-07-05T14:57:11","modified_gmt":"2011-07-05T12:57:11","slug":"average-mean-versus-median","status":"publish","type":"post","link":"https:\/\/ingmarverheij.com\/en\/average-mean-versus-median\/","title":{"rendered":"Average : Mean versus Median"},"content":{"rendered":"

\"I<\/a>The average of a set of numbers is a commonly used, but the defintion of average is poorly understood and can raise the risk of being manipulated.<\/p>\n

The average of a set of numbers can be determined with the mean<\/strong> or the median<\/strong>. To better understand the difference between mean and median I will explain the definition of both and illustrate it with examples.<\/p>\n

<\/p>\n

The difference between mean and median<\/h4>\n

Understanding the difference between the mean and median allows you to take advantage of one another and prevent the risk of being manipulated<\/strong>. To illustrate the difference<\/strong> we\u2019ll take this set of 5 numbers:<\/p>\n

4  2  14  2  3<\/font><\/strong><\/p>\n

Mean<\/h5>\n

The mean is the also known as the arithmetic<\/strong> mean<\/strong> and is calculated by adding N numbers in a data set together and dividing it by N<\/strong>. The mean of the 5 numbers above is 5.0<\/strong><\/p>\n

4 + 2 + 14 + 2 + 3 \/ 5 = 5.0<\/strong><\/p>\n

Median<\/h5>\n

The median of a data set is the middle<\/strong> number when the set is sorted in numerical order. With an odd-numbered data set this is the number that is in the middle. When there is an even-numbered data set the mean of the two middle numbers is taken. The median of the 5 numbers above is 3.0<\/strong><\/p>\n

Odd-numbered : 2 + 2 + 3<\/strong> + 4 + 14 = 3.0<\/strong><\/p>\n

Even-numbered: 2 + 2 + 3 + 4<\/strong> + 5 + 14 = (3 + 4) \/ 2 = 3.5<\/strong><\/p>\n

 <\/p>\n

When to use what<\/h4>\n

In most cases the arithmetic mean<\/strong> is used as the average<\/strong> of a data set since it will the take all numbers in the data set in the calculation. In other words, each number in the data set has influence<\/strong> on the outcome. If this outcome should not be influenced by spikes<\/strong> (high or low) the median will give a better result.<\/p>\n

 <\/h5>\n
An example<\/h5>\n

A small town with 500 residents earn roughly  \u20ac 50,000.- per year. Both the median and mean are around \u20ac 50.000,-. Now a (super wealthy) family moves in to town, their income is around \u20ac 1 Billion<\/strong> a year.<\/p>\n

The median income stays around \u20ac 50.000,- per year (since all 500 others stil earn around \u20ac 50.000,- per year) but the aritmethic mean is \u20ac2.025 million!<\/strong> <\/p>\n

Although nothing has changed<\/strong> for the 500 citizens, the way the numbers are presented might affect them. For instance when the tax paid is based on the average income (\u2026).<\/p>\n

 <\/p>\n

Service levels \/ performance metrics \/ ROI<\/h4>\n

Now what happens if we take this knowledge to our daily<\/strong> lives? There are numerous of examples where the average of a set of numbers is used. For instance \u201cThe average response time was 100 milliseconds, that\u2019s great!\u201d or \u201cThe average load on server X was 10% so the request to order a new server is denied<\/strong>.\u201d<\/p>\n

 <\/p>\n

Conclusion<\/h4>\n

Juggling<\/strong> with numbers is easy, the result can be transformed into a better suiting result (for the presenter<\/strong>) just by using a different methodology of calculating the average. Knowing the difference in mean and median can help you prevent<\/strong> being misled or manipulated<\/strong>, it might even help you<\/strong> doing so. <\/p>\n

 <\/p>\n

Ingmar Verheij<\/p>","protected":false},"excerpt":{"rendered":"

The average of a set of numbers is a commonly used, but the defintion of average is poorly understood and can raise the risk of being manipulated. The average of a set of numbers can be determined with the mean or the median. To better understand the difference between mean and median I will explain […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-container-style":"default","site-container-layout":"default","site-sidebar-layout":"default","disable-article-header":"default","disable-site-header":"default","disable-site-footer":"default","disable-content-area-spacing":"default","footnotes":""},"categories":[302],"tags":[351,353,352],"class_list":["post-2910","post","type-post","status-publish","format-standard","hentry","category-performance-testing","tag-average","tag-performance-metrics","tag-statistics"],"_links":{"self":[{"href":"https:\/\/ingmarverheij.com\/en\/wp-json\/wp\/v2\/posts\/2910","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ingmarverheij.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ingmarverheij.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ingmarverheij.com\/en\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ingmarverheij.com\/en\/wp-json\/wp\/v2\/comments?post=2910"}],"version-history":[{"count":0,"href":"https:\/\/ingmarverheij.com\/en\/wp-json\/wp\/v2\/posts\/2910\/revisions"}],"wp:attachment":[{"href":"https:\/\/ingmarverheij.com\/en\/wp-json\/wp\/v2\/media?parent=2910"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ingmarverheij.com\/en\/wp-json\/wp\/v2\/categories?post=2910"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ingmarverheij.com\/en\/wp-json\/wp\/v2\/tags?post=2910"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}