What is Mean?

Mean Formula

You are free to use this image on you website, templates, etc., Please provide us with an attribution linkHow to Provide Attribution?Article Link to be HyperlinkedFor eg:Source: Mean Formula (wallstreetmojo.com)

The arithmetic mean formula is calculated by adding all the available periodic returns and dividing the result by the number of periods.

where Ri = return in the ith year and n = Number of periods

The geometric meanGeometric MeanGeometric Mean (GM) is a central tendency method that determines the power average of a growth series data. read more formula is calculated by initially adding one to each of the available periodic returns, then multiplying them and raising the result to the power of the reciprocal of the number of periods, and then deducting one from it.

Calculation of Mean (Step by Step)

Steps to Calculate Arithmetic Mean

  • Step 1: Firstly, determine the returns for various periods based on the portfolio’s value or investment at various times. The returns are denoted by r1, r2, ….., rn corresponding to 1st year, 2nd year,…., nth year.Step 2: Next, determine the number of periods denoted by n.Step 3: Finally, the arithmetic average of returns is calculated by adding all the periodic returns and dividing the result by the number of periods, as shown above.

Steps to Calculate Geometric Mean

  • Step 1: First, determine the various periodic returns denoted by r1, r2, ….., rn corresponding to 1st year, 2nd year,…., nth year.Step 2: Next, determine the number of periods denoted by n.Step 3: Finally, the geometric average of returns is calculated by initially adding one to each of the available periodic returns, then multiplying them and raising the result to the power of the reciprocal of the number of periods, and then deducting one from it as shown above.

Examples

Calculate the arithmetic and geometric mean of the annual returnsAnnual ReturnsThe annual return is the income generated on an investment during a year as a percentage of the capital invested and is calculated using the geometric average. This return provides details about the compounded return earned yearly and compares the returns supplied by various investments like stocks, bonds, derivatives, mutual funds, etc.read more based on the given information.

Return of 1st year, r1

  • Return of 1st year, r1 = [(Closing stock price / Opening stock price) – 1] * 100%= [($110.15 / $100.00) – 1] * 100%= 10.15%

Similarly, we have calculated the returns for the year as follows:

Return of 2nd year, r2 = [($117.35 / $110.15) – 1] * 100%

= 6.54%

Return of 3rd year, r3 = [($125.50 / $117.35) – 1] * 100%

= 6.95%

Return of 4th year, r4 = [($130.10 / $125.50) – 1] * 100%

= 3.67%

Return of 5th year, r5 = [($140.00 / $130.10) – 1] * 100%

= 7.61%

Therefore, the calculation of the arithmetic mean equation is as follows:

  • Arithmetic mean = (r1 + r2 + r3 + r4 + r5) / n= (10.15% + 6.54% + 6.95% + 3.67% + 7.61%) / 5

The Arithmetic Average of Returns will be:

Now, the calculation of geometric average equation is done as follows:

  • Geometric mean = [(1 + r1) * (1 + r2) * (1 + r3) * (1 + r4) * (1 + rn)] 1/n – 1= [(1 + 10.15%) * (1 + 6.54%) * (1 + 6.95%) * (1 + 3.67%) * (1 + 7.61%)] 1/5 – 1

The Geometric Average of Returns will be:

Therefore, the arithmetic and the geometric mean of the returnsGeometric Mean Of The ReturnsGeometric Mean Return, also known as Geometric Average Return, is a metric used to calculate the average rate of return for, precisely, the investments that are compounded over different periods. It does not need investment amount but only return figures to evaluate the performance of an investment. read more are 6.98% and 6.96% respectively.

Relevance and Uses

From the perspective of an analyst, an investor, or any other financial user, it is very important to understand the concept of mean, a statistical indicator used to estimate a company’s stock performance over a certain period, which can be days, months, or years.

Mean Formula In Excel (with excel template)

Now, let us take the example of the stock prices of Apple Inc. for 20 days to illustrate the concept of mean in the Excel template below.

The calculation of the arithmetic mean is as follows:

The geometric mean is as follows:

The table provides a detailed calculation of the arithmetic and geometric mean.

This article is a guide to Mean Formula. Here, we learn how to calculate arithmetic and geometric mean using its formulas for the company’s annual returns. You can learn more about our articles from the following: –

  • Calculate Weighted MeanCalculate Weighted MeanThe Weighted Mean equation is a statistical method determining the average by multiplying the weights with their respective mean and taking its sum. It is an average in which weights are assigned to individual values determining each observation’s relative importance. Weighted Mean = ∑ni=1 (xi*wi)/∑ni=1wi
  • read moreHarmonic MeanHarmonic MeanHarmonic Mean is the reciprocal of the arithmetic mean of the reciprocal of numeric values. This is calculated by dividing the number of values in a given dataset by the sum of every value’s reciprocals. read moreVariance vs Standard DeviationVariance Vs Standard DeviationVariance is a numeric value that defines every observation’s variability from the arithmetic mean, while Standard Deviation is a measure to determine how spread out the observations are from the arithmetic mean. read moreMean vs MedianMean Vs MedianMean is an average of given numbers. It sums up the numbers and divides them with the count of numbers which provides us with the mean. On the other hand, the median returns the middle number from the whole data set.read more