Mean Examples

Examples of Mean

Mean is the most commonly used measure in central tendency. There are many examples of mean which can be calculated based on the availability and requirement of data  – Arithmetic mean, weighted mean, Geometric Mean and Harmonic mean.

Mean-Examples

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

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:

Arithmetic Mean = Sum of Total Numbers / Number of Values

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 –

Mean Example 1

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

Mean = 17

This 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 are being given an equal weight of 1/7. Suppose if all the values have different weight, 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 among the two available options

  • Option 1: The Canon camera gets 8 points for Image Quality, 6 points for Battery Life, 7 points for the zoom range.
  • Option 2: The Nikon camera gets 9 points for Image Quality, 4 points for Battery Life, 6 points for zoom range

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

Solution:

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

Mean Calculation 2

Total Weighted Average = 7.2

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

Mean Example 2.1

Total Weighted Average =6.9

In this, we cannot calculate the mean of the points for the solution as weights are there for all the Factors.

It can be recommended based on the weighting factor of Fin that he should go for Canon camera as its weighted average is more.

Example #3 – Geometric Mean

This method of mean calculation is usually used for growth rates like population growth rate or interest rates. On the one hand, arithmetic mean adds items, whereas geometric mean multiplies items.

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

Solution:

It can be calculated using the formula of geometric mean, which is:

Geometric Mean ( X )= N√(X1*X2*X3………….XN)

So geometric mean will be –

Mean Calculation 3

=(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 geometric mean will be –

Mean Example 3.1

It will be calculated as:

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

Mean = 0.35

Suppose Fin’s salary jumped from $2500 to $5000 over the course of ten years. Using the geometric mean, calculate his average yearly increase.

So, the calculation of geometric mean will be –

Mean Calculation 3.2

=(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

Harmonic mean is another type of numerical average, which is calculated by way of dividing the number of observations available by reciprocal of each number present in the series. So, in 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 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 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 being invested in High International Ltd and rest 80% amount being 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 index.

Solution:

In order to calculate the PE ratio of the index, the P/E ratio of the two companies will be calculated firstly.

P/E Ratio = Market Capitalization / Earnings

So, the calculation of P/E ratio for High International Ltd will be –

Mean Example 4

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

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

So, the calculation of P/E ratio for Low International Ltd will be –

Mean Calculation 4.1

P/E ratio (Low International Ltd) = $ 0.5 / $ .002 billion

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

Calculation of P/E ratio of 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)

So, the calculation of Weighted arithmetic mean will be –

Mean Example 4.2

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 Weighted Harmonic Mean will be –

Mean Calculation 4.3

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

Weighted Harmonic Mean = 89.29

From the above, it can be observed that the weighted arithmetic mean of the data significantly overestimates the price-earnings ratio mean calculated.

Conclusion

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

Reader Interactions

Leave a Reply

Your email address will not be published. Required fields are marked *