## Definition of Mean Example

Mean in the statistical parlance can be referred to as the mathematical arithmetic or geometric average which can be calculated for a set of 2 or more timely returns.

However, there as mentioned in the definition there is more than a single way for the calculation of the average or the mean for a certain given set of data or given a set of numbers that shall include the methods of the geometric mean and the arithmetic mean.

The equation or the formula for a mean or average of returns based on the arithmetic mean can be calculated by summing up all the available periodic returns or all the given observations and divide that result by the number of observations or number of periods.

### Examples of Mean

Below are the examples of the mean:

#### Mean Example – #1

XYZ stock has been performing quite well for a couple of years but the investors are a little skeptical as to whether the stock would perform the same in the future as in recent weeks it has remained volatile as one of the key personnel of the company has resigned and the market has started doubting about the future of the company.

Axel wants to invest in XYZ stock and has approach a financial advisor to advise on XYZ stock. Before taking any decision, the advisor calculates the mean of the weekly returns.

**Solution:**

We are given weekly returns of the XYZ stock and now we need to calculate the average of this weekly data which is for 9 weeks.

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The formula for computing the average or mean return is the sum of all data and dividing the same by a number of observations. and the Number of Observations is 9

**Mean = Total / Number of Observation**

Mean = -1.37% / 9

Mean = **-0.15%**

Hence, the mean weekly return would be -1.37% dividing the same by 9 will yield -0.15% average return for XYZ stock.

#### Mean Example -2

Suhas is the MD of Vatsal enterprises and he is seeing that his sales are variable for every month and he wants to know the average quarterly sales and wants to identify the quarter in which the sales are the most.

Below are the monthly sales data extracted from accounting software. You are required to compute the quarterly arithmetic average.

**Solution:**

We are given monthly sales and therefore we will take the sum of 3 months starting from January and then for each total, we will divide it by 3 which shall give us the quarterly average sales figure.

**Mean = Total / Number of Observation**

The highest average is for the 1^{st} quarter and hence that quarter is the best performing for the company.

#### Mean Example – #3

Jack Hemsley has recently graduated, and his field of interest lies in the stock market. He has been observing Alpha stock for quite some time and wants to calculate the daily average return as he feels he can now trade into the same and can make some money out of it. Jill his friend advises him first to know what return he can expect when he starts trading, therefore he suggests him to compute the average this stock has given. Jack decides to use a geometric average of over arithmetic average. You are required to compute geometric mean based on the below data for the last 5 days.

**Solution:**

To compute geometric return, we need to take the product of the return and then take the 4^{th} root of the result and subtract the same from 1 will yield us the geometric return.

- Geometric mean = [ (1+0.0909) * (1-0.0417) * (1+0.0174) * (1-0.0043) ]
^{1/4}– 1 **1.45%**

#### Mean Example – #4

Below is the sample of 5 children who are aging 10 years old and their height data is given. You are required to compute both the arithmetic mean and geometric mean and compare both and comment upon the same.

**Solution:**

To compute geometric return, we need to take the product of the observations and then take the 5^{th} root of the result and subtract the same from 1 will yield us the geometric return.

- Geometric mean = [ (1+120) * (1+110) * (1+100) * (1+90) * (1+105) ]
^{1/5}– 1 **104.52**

The formula for computing the average or mean return is the sum of all data and dividing the same by the number of observations, and the number of observations is 5.

**Arithmetic Mean = Total / Number of Observations**

- Arithmetic Mean = 525/5
- Arithmetic Mean=
**105**

The geometric mean is less than the arithmetic means and is generally the case and it cannot be more than the arithmetic mean.

### Conclusion

Average or mean are used and computed almost daily and for many different reasons especially in the field of the capital market, science, statistics, etc. Using the appropriate average is the key and this matter is based upon an understanding of the data. Geometric average considers compounding whereas arithmetic average considers simple summation. Hence where growth is expected to be known geometric is best and where values are not much volatile and not much spread arithmetic average can be used.

### Recommended Articles

This is has been a guide to the Mean Example. Here we have discussed the Definition along with various examples of Mean with Geometric mean and Arithmetic Mean. You may also have a look at the following articles to learn more –