#quantitative-methods-basic-concepts #statistics
Weighted Mean
The weighted mean is computed by weighting each observed value according to its importance. In contrast, the arithmetic mean assigns equal weight to each value. Notice that the return of a portfolio is the weighted mean of the returns of individual assets in the portfolio. The assets are weighted on their market values relative to the market value of the portfolio. When we take a weighted average of forward-looking data, the weighted mean is called
expected value.
If you want to change selection, open original toplevel document below and click on "Move attachment"
Parent (intermediate) annotation
Open itWeighted Mean
The weighted mean is computed by weighting each observed value according to its importance. In contrast, the arithmetic mean assigns equal weight to each value. Notice that the return of a portfolio is the weighted mean of the returns of individual assets in the portfolio. The assets are weighted on their market values relative to the market value of the portfolio. When we take a weighted average of forward-looking data, the weighted mean is calledexpected value.
Example
A year ago, a certain share had a price of $6. Six months ago, the same share had a price of $6.20. The share is now trading at $7.50. Because the most recentOriginal toplevel document
Subject 4. Measures of Center Tendencymean will always be less than the arithmetic mean. The more dispersed the rates of returns, the greater the difference between the two. This measurement is not as highly influenced by extreme values as the arithmetic mean.
<span>Weighted Mean
The weighted mean is computed by weighting each observed value according to its importance. In contrast, the arithmetic mean assigns equal weight to each value. Notice that the return of a portfolio is the weighted mean of the returns of individual assets in the portfolio. The assets are weighted on their market values relative to the market value of the portfolio. When we take a weighted average of forward-looking data, the weighted mean is calledexpected value.
Example
A year ago, a certain share had a price of $6. Six months ago, the same share had a price of $6.20. The share is now trading at $7.50. Because the most recent price is the most reliable, we decide to attach more relevance to this value. So, suppose we decide to "weight" the prices in the ratio 1:2:4, so that the current share price is twice as important as the price from six months ago, which in turn is twice as important as the price from last year.
The weighted mean would then be: (1 x 6 + 2 x 6.2 + 4 x 7.5) / (1 + 2 + 4) = $6.91. If we calculated the mean without weights, we'd get: (6 + 6.2 + 7.5) / 3 = $6.57. The fact that we've given more importance to the most recent (higher) share price inflates the weighted mean relative to the un-weighted mean.
Median
In English, the word "mediate" means to go between or to stand in the middle of two groups, in order to act as a referee, so to speak. The median doeSummary
| status | not read | | reprioritisations | |
|---|
| last reprioritisation on | | | suggested re-reading day | |
|---|
| started reading on | | | finished reading on | |
|---|
Details