- Descriptive Vs. Inferential Statistics
- Types of Measurement Scales
- Parameter, Sample Statistic, and Frequency Distribution
- Relative Frequencies and Cumulative Relative Frequencies
- Properties of a Data Set (Histogram / Frequency Polygon)
- Measures of Central Tendency
- Calculating Arithmetic Mean
- Calculating Weighted Average Mean
- Calculating Geometric Mean
- Calculating Harmonic Mean
- Calculating Median and Mode of a Data Set
- Quartiles, Quintiles, Deciles, and Percentiles
- Range and Mean Absolute Deviation
- Variance and Standard Deviation
- Chebyshev’s Inequality
- Coefficient of Variation
- Sharpe Ratio
- Skewness and Kurtosis
- Relative Locations of Mean, Median and Mode
Calculating Weighted Average Mean
One characteristic of an arithmetic mean is that all observations have equal weight (=1/N). However, this may not always be the case. In some cases, different observations may influence the mean differently. This has special relevance in portfolios where a portfolio is made up of different stocks each having a different weight.
Let’s assume that we have a portfolio comprising three stocks, A, B and C as follows:
| Stock | Returns | Weight |
| A | 12% | 20% |
| B | 18% | 30% |
| C | 24% | 50% |
We have the stock returns for each stock and the weight of each stock in the portfolio. For example, if the investor has a total of $1,000 invested in the portfolio, 20% or $200 is invested in Stock A, $300 is invested in stock B, and the remaining $500 is invested in Stock C.
The weighted average mean is calculated using the following formula:
The weighted mean of our portfolio will be calculated as follows:
Note that the weighted mean is closer to the returns from Stock C because Stock C has more influence (weight) on the portfolio.
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