@mathematics.proofs 4 October 2020 edited more from that month

Financial Mathematics: How to Calculate the Mean Deviation Just a few days ago, I demonstrated **how to calculate the mean** of a set of numbers and I also explained the definition of the term mean. https://tinyurl.com/y3ufh5v3 In this article, I'll be showing you **how to calculate the** ****mean deviation**** of a set of values. By calculating the mean deviation of a set of values, you will come to terms with the definition of mean deviation. The contents of this article may be useful in **financial mathematics**. It will allow you to calculate the mean deviation for various numbers of observations and within any given time frame. The limits? Well, your computing power and programming knowledge.

*Image by* *Deedster* *from Pixabay* https://pixabay.com/users/deedster-2541644/?utm_source=link-attribution&utm_medium=referral&utm_campaign=image&utm_content=1462878 So, let's say you have the set of values: **x = {5, 6, 6, 7, 4, 3, 4, 8, 5, 6, 7, 5, 5, 4, 5}** The number of observations (n) here would be: **15** Therefore, the mean would be: **(5+6+6+7+4+3+4+8+5+6+7+5+5+4+5)/15 = 5.33** (to 2 decimal places) Now, with mean deviations, you have to calculate how much **each value** in a set of values **deviates from the mean**. You get all these **differences**, then you **divide by the** ****original number**** **of observations**. Let me demonstrate how this will be done in this case: Firstly, let me organise our current set of data: **x = {3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8}** Here, the number of observations (n) **is still 15**. Nothing has changed in terms of observations. Our original set of values haven't changed either. The only difference is, they are **organised**. In this set of data, we have the numbers 3, 4, 5, 6, 7 and 8. 3 appears once, 4 appears three times, 5 appears five times, 6 appears three times, 7 appears two times and 8 appears once. Now the difference between 3 and 5.33 is **2.33**. | 3 - 5.33 | = 2.33 The difference between 4 and 5.33 is **1.33**. | 4 - 5.33 | = 1.33 The difference between 5 and 5.33 is **0.33**. | 5 - 5.33 | = 0.33 The difference between 6 and 5.33 is **0.67**. | 6 - 5.33 | = 0.67 The difference between 7 and 5.33 is **1.67**. | 7 - 5.33 | = 1.67 And, finally, the difference between 8 and 5.33 is **2.67**. | 8 - 5.33 | = 2.67

*Image by* *Qualityrendersmicrostock* *from Pixabay* https://pixabay.com/users/qualityrendersmicrostock-13404983/?utm_source=link-attribution&utm_medium=referral&utm_campaign=image&utm_content=4922336 As the numbers in our set of data have **different frequencies**, the mean deviation would look like this: **Mean Deviation ≈ (1*2.33 + 3*1.33 + 5*0.33 + 3*0.67 + 2*1.67 + 1*2.67)/15** 1 + 3 + 5 + 3 + 2 + 1 = 15 (matching our number of observations) So in this case, the mean deviation would be approximately: **Mean Deviation ≈ (2.33 + 3.99 + 1.65 + 2.01 + 3.34 + 2.67)/15 ≈ 1.07** In other words, on average, the deviation is 1.07, approximately. **Video related to article:** https://youtu.be/T8VcdpfP7NU I hope this article has helped you understand what a mean deviation is. **For more mathematics resources**, feel free to check out the **links below**. *Article by Tiago Hands:* *https://www.instagram.com/tiago_hands* *Mathematics Proofs (Instagram):* *https://www.instagram.com/mathematics.proofs* *Mathematics Youtube Channel:* *https://www.youtube.com/c/mathsvideosforweb/videos* *Read.Cash Mathematics:* *https://read.cash/@mathematics.proofs*