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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.

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*

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*

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:**

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*

Nice post