. <\/strong>The most common one is the mean.\u00a0 Let’s look at it with an example:<\/p>\nLet’s say we want to know how many pens 5 friends have in their offices:<\/p>\n
Person#1 has 2<\/p>\n
Person#2 has 3<\/p>\n
Person#3 has 4<\/p>\n
Person#4 has 7<\/p>\n
Person#5 has 9<\/p>\n
The total amount of pens is 2+3+4+7+9 = 25 pens<\/p>\n
n represents our population and is equal to 5 people<\/p>\n
The mean is the total amount of pens divided by the total amount of people. 25 divided by 5 = 5 pens.<\/p>\n
Sometimes this number can be decimal, like 1.8 pens.<\/p>\n
I know what you might be thinking: “How can one have 1.8 pens?”, for now, let’s leave this as a rough approximation, as we would say something like there are on average 2 pens each person has at their office. But keep this concept in mind as we are translating real-life examples to math and sometimes we need rough approximations.<\/p>\n
In our specific case, each person has on average 5 pens inside their office.<\/p>\n
To calculate the standard deviation we:<\/p>\n
1. subtract the mean from the number<\/p>\n
2. square this difference<\/p>\n
3. divide the result by n<\/p>\n
4. square root the result<\/p>\n
After this step we will obtain two different measurements:<\/p>\n
Variance = sum of all results divided by the population<\/p>\n
Standard deviation = square root of the variance<\/p>\n
Here our variance is 6.8 and our standard deviation is 2.6<\/p>\n
The common greek letter for standard deviation is\u00a0 \u03c3<\/span><\/span><\/p>\nSo \u03c3 = 2.6<\/span><\/span><\/p>\n[\/et_pb_text][et_pb_image src=”http:\/\/euseguros.pt\/wp-content\/uploads\/2021\/10\/standard-deviation.jpg” _builder_version=”4.4.3″][\/et_pb_image][et_pb_text _builder_version=”4.4.3″]<\/p>\n
What does this tell us?<\/strong><\/h3>\nThe mean is 5 pens and the standard deviation is 2.6<\/p>\n
There are 3 percentiles to know in regards to the standard deviation, assuming the data is normally distributed:<\/p>\n
68% of the data falls withing +\/- 1 standard deviation from the mean<\/p>\n
90% of the data falls withing +\/- 2 standard deviation from the mean<\/p>\n
99.7 % of the data falls withing +\/- 3 standard deviation from the mean<\/p>\n
Average results, fall within 1 standard deviation of the mean( + or -), outlier results fall within at least 2 standard deviations from the mean. Something like 1, 1, 1, 1, 1, 1, 40 (40 is an outlier. Same thing if it was a negative number)<\/p>\n
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So, coming back to our example, knowing that 68% of the data falls within 1 standard deviation, we can then say that 3 people have between (5-2.6, 5+2.6) or rounding up (2.4 to 7.6) pens in their offices.<\/p>\n
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Standard deviation tells us how spread out the data is. It’s used with data normally distributed and tells us how skinny or wide it is.<\/p>","protected":false},"author":1,"featured_media":6491,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[105],"tags":[221,223,220,222,225,219,224],"yoast_head":"\n
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