## Examples of Mean

Mean example will be as there are different number in data we shall add values of all the numbers and divide it by the number of values like there are five numbers having value of one, two, three, four, and five and to calculate the mean the sum of all values is fifteen which will be divided by five and the mean is resultant value which is three.

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. Let us discuss these examples of mean in detail –

### Top 4 Examples of Mean

Below are the examples of the 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 mean will be –

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

**Mean = 17**

This mean is 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 example, 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 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 he should 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 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 the 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 short harmonic mean 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 the $ 50 billion market capitalization and $ 2 billion earnings. On the other hand, Low international Ltd has the $ 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 ratio 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 example it can be observed that weighted arithmetic mean of the data significantly overestimates price-earnings ratio mean calculated.

### Conclusion

From the above-discussed mean examples, we can conclude the following –

- The arithmetic mean can be used to calculate the normal average if there is no weight for each value or factors. Its major disadvantage is that it is sensitive to extreme values especially if we are having a smaller sample size. 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 if 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 Geometric mean harmonic mean is not affected by sample fluctuations.

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