Examples of Mean

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Top 4 Examples of Mean

Example #1 – Arithmetic Mean

Suppose a set of data containing the following numbers:

8, 16, 15, 17, 18, 20, 25

We have to calculate the mean for the above set.

Solution:

So, the calculation of arithmetic meanCalculation Of Arithmetic MeanArithmetic mean denotes the average of all the observations of a data series. It is the aggregate of all the values in a data set divided by the total count of the observations.read more will be –

In this case it will be (8 + 16 + 15 + 17 + 18 + 20 + 25)/7 which comes to 17.

Mean = 17

It means the simple arithmetic mean as none of the data in the sample are repeating, i.e., ungrouped data.

Example #2 – Weighted Average Mean

In the above, all the numbers gave an equal weight of 1/7. Suppose all the values have different weights. Then the mean will be pulled by the weight.

Suppose Fin wants to buy a camera, and he will decide among the available option based on their features as per the following weights:

  • Battery Life 30 %Image Quality 50 %Zoom Range 20 %

He is confused about the two available options:

  • Option 1: The Canon camera gets 8 points for image quality, 6 points for battery life, and 7 points for the zoom range.Option 2: The Nikon camera gets 9 points for image quality, 4 points for battery life, and 6 points for zoom range.

Which camera should he go for? The above points are on 10-point ratings.

The calculation of the total weighted average for Canon will be: 

Total Weighted Average = 7.2

The calculation of the total weighted average for Nikon will be –

Total Weighted Average =6.9

We cannot calculate the mean of the points for the solution as weights are there for all the factors.

Based on Fin’s weighting factor, one can recommend that he go for the Canon camera as its weighted average is more.

Example #3 – Geometric Mean

This method of mean calculation is usually for growth rates like population or interest rates. On the one hand, arithmetic means adding items, whereas geometric meanGeometric MeanGeometric Mean (GM) is a central tendency method that determines the power average of a growth series data. read more multiplies items.

Calculate the geometric mean of 2, 3, and 6.

One can calculate it using the formula of geometric mean, which is:

So geometric mean will be –

=(2 * 3 * 6)^1/3

Mean = 3.30

Calculate the geometric mean for following a set of data:

1/2, 1/5, 1/4, 9/72, 7/4

So, the geometric mean will be:

One can calculate it as follows:

(1/2 * 1/5 * 1/4 * 9/72 * 7/4)^1/5

Mean = 0.35

Suppose Fin’s salary jumped from $2,500 to $5,000 over ten years. Then, using the geometric mean, calculate his average yearly increase.

So, the calculation of the geometric mean will be:

=(2500 * 5000)^1/2

Mean = 3535.534

The above mean is the increase over 10 years. Therefore, the average increase over 10 years will be 3535.534/10, i.e., 353.53

Example #4 – Harmonic Mean

The harmonic mean is another numerical average calculated by dividing the number of observations available by the reciprocal of each number present in the series. So, the short harmonic 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 more is the reciprocal of the arithmetic mean of reciprocals.

Let us take an example of two firms in the market: High International Ltd. and Low International Ltd. High International Ltd. has a $50 billion market capitalization and $2 billion in earnings. On the other hand, Low International Ltd. has a $0.5 billion market capitalization and $2 million in earnings. Suppose one index is made by considering the stocks of the two companies High International Ltd. and Low international Ltd., with the 20% amount invested in High International Ltd. The remaining 80% amount is invested in Low International Ltd.

Calculate the PE ratioPE RatioThe price to earnings (PE) ratio measures the relative value of the corporate stocks, i.e., whether it is undervalued or overvalued. It is calculated as the proportion of the current price per share to the earnings per share. read more of the stock indexStock IndexThe stock index, which is also known as the stock market index, is a tool used to determine the performance of shares/securities in the market and to calculate the return on the stock of their investment investors use it to have knowledge about the performance of investments and access the total value they possess.read more.

The P/E ratio of the two companies will be calculated first to calculate the PE ratio of the index.

P/E Ratio = Market CapitalizationMarket CapitalizationMarket capitalization is the market value of a company’s outstanding shares. It is computed as the product of the total number of outstanding shares and the price of each share.read more / Earnings

So, the calculation of the P/E ratio for High International Ltd. will be as follows:

P/E ratio (High International Ltd.) = $50 / $2 billion

P/E Ratio (High International Ltd.) = $25 billion.

So, the calculation of the weighted arithmetic mean will be:

P/E ratio (Low International Ltd.) = $0.5/$ 0.002 billion

P/E ratio (Low International Ltd.)= $250

Calculation of the P/E ratio of the index using:

#1 – Weighted Arithmetic Mean:

Weighted Arithmetic Mean = (Weight of investment in High International Ltd. * P/E ratio of High International Ltd.) + (Weight of investment in Low International Ltd. * P/E ratio of Low International Ltd.)

Weighted Arithmetic Mean = 0.2 * 25 + 0.8 * 250

Weighted Arithmetic Mean = 205

#2 – Weighted Harmonic Mean:

Weighted Harmonic Mean = (Weight of investment in High International Ltd. + Weight of investment in Low International Ltd.) / [(Weight of investment in High International Ltd. / P/E ratio of High International Ltd.) + (Weight of investment in Low International Ltd. / P/E ratio of Low International Ltd.)]

So, the calculation of the weighted harmonic mean will be:

Weighted Harmonic Mean = (0.2 + 0.8) / (0.2/25 + 0.8/250)

Weighted Harmonic Mean = 89.29

From the above, one can observe that the weighted arithmetic mean of the data significantly overestimates the price-earnings ratio mean calculated.

Conclusion

  • The arithmetic mean can be used to calculate the averageCalculate The AverageAverage is the value that is used to represent the set of values of data as is the average calculated from whole data and this formula is calculated by adding all the values of the set given, denoted by summation of X and dividing it by the number of values given in set denoted by N.read more if there is no weight for each value or factor. Its major disadvantage is that it is sensitive to extreme values, especially if we have a smaller sample sizeSample SizeThe sample size formula depicts the relevant population range on which an experiment or survey is conducted. It is measured using the population size, the critical value of normal distribution at the required confidence level, sample proportion and margin of error.read more. It is not at all appropriate for skewed distribution.A geometric mean method is when a value changes exponentially. The geometric mean cannot be used in any of the values in the data is zero or less than zero.The harmonic mean is used when small items have to be given greater weight. It is suitable for calculating the average rate, time, ratios, etc. Like the geometric mean, sample fluctuations do not affect the harmonic mean.

This article has been a guide to Mean Examples. Here, we discuss how to calculate the mean with the help of practical examples, along with a detailed explanation. You can learn more about finance from the following articles: –

  • Geometric Mean vs Arithmetic MeanMean vs MedianPopulation Mean FormulaBills of Exchange Overview