## 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.

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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:**

**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 –

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 –

**Total Weighted Average = 7.2**

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

**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}√(X_{1}*X_{2}*X^{3}………….X_{N})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 geometric mean will be –

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 –

=(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 –

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 –

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 –

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 –

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

- The arithmetic mean can be used to calculate the average 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 to be used when a value changes exponentially. Geometric mean cannot be used in any of the values in the data is zero or less than zero.
- The harmonic mean is to be used when small items have to be given greater weight. It is suitable for calculating the average of Rate, time, ratios, etc. Like the Geometric mean harmonic mean is not affected by sample fluctuations.

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