Financial Mathematics: How to Calculate the Mean Deviation

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3 years ago

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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.

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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.

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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.