Positive Skew
Negative Skew
Sources:
http://www.brendan.com/glossary.html
http://cnx.org/content/m11011/latest/
Tuesday, April 15, 2008
Skewness
Skewness is an asymmetrical frequency distribution in which the values are concentrated on one side of the central tendency and trail out on the other side. If the trail is to the right or positive end of the scale, the distribution is said to be positively skewed. If the distribution trails off to the left or negative side of the scale, it is said to be negatively skewed.
Positive Skew
Negative Skew
Sources:
http://www.brendan.com/glossary.html
http://cnx.org/content/m11011/latest/
Positive Skew
Negative Skew
Sources:
http://www.brendan.com/glossary.html
http://cnx.org/content/m11011/latest/
Friday, April 4, 2008
Measures of Central Tendency
Central Tendency: The center or middle of a distribution. There are many measures of central tendency. The most common are the mean, median, and mode.
Mode
The mode is the most frequently-occurring value (or values).
To calculate the mode:- Calculate the frequencies for all of the values in the data.
- The mode is the value (or values) with the highest frequency.
Median
The median is the midpoint of a distribution: the same number of observations are above the median as below it
To calculate the median:- Sort the values into ascending order.
- If you have an odd number of values, the median is the middle value.
- If you have an even number of values, the median is the arithmetic mean (see above) of the two middle values.
Wednesday, March 26, 2008
Tuesday, March 25, 2008
Harmonic Mean
Formula:
Description:
The harmonic mean is the number of variables divided by the sum of the reciprocals of the variables. Typically, it is appropriate for situations when the average of rates is desired.
Example:
For instance, if for half the distance of a trip you travel at 40 kilometres per hour and for the other half of the distance you travel at 60 kilometres per hour, then your average speed for the trip is given by the harmonic mean of 40 and 60, which is 48; that is, the total amount of time for the trip is the same as if you travelled the entire trip at 48 kilometres per hour. If you had travelled for half the time at one speed and the other half at another, the arithmetic mean, in this case 50 kilometres per hour, would provide the correct average.
In finance, the harmonic mean is used to calculate the average cost of shares purchased over a period of time. For example, an investor purchases $1000 worth of stock every month for three months and the prices paid per share each month were $8, $9, and $10, then the average price the investor paid is $8.926 per share. However, if the investor purchased 1000 shares per month, the arithmetic mean (which turns out to be $9.00) would be used. Note that in this example, the investor buying $1000 worth of the stock each month means buying 125 shares at $8 the first month, 111.11 shares at $9 the second month, and 100 shares at $10 in the third month. Fewer shares are purchased at higher prices while more shares are purchased at lower prices. Thus more weight is given to the lower prices than the higher prices in the calculation of the average cost per share ($8.926). If the investor had instead purchased 1000 shares each month then equal weight would be given to high and low purchase prices, leading to an average cost per share of $9.00. This explains why the harmonic mean is less than the arithmetic mean.
Sources:
http://en.wikipedia.org/wiki/Harmonic_mean
Description:
The harmonic mean is the number of variables divided by the sum of the reciprocals of the variables. Typically, it is appropriate for situations when the average of rates is desired.
Example:
For instance, if for half the distance of a trip you travel at 40 kilometres per hour and for the other half of the distance you travel at 60 kilometres per hour, then your average speed for the trip is given by the harmonic mean of 40 and 60, which is 48; that is, the total amount of time for the trip is the same as if you travelled the entire trip at 48 kilometres per hour. If you had travelled for half the time at one speed and the other half at another, the arithmetic mean, in this case 50 kilometres per hour, would provide the correct average.
In finance, the harmonic mean is used to calculate the average cost of shares purchased over a period of time. For example, an investor purchases $1000 worth of stock every month for three months and the prices paid per share each month were $8, $9, and $10, then the average price the investor paid is $8.926 per share. However, if the investor purchased 1000 shares per month, the arithmetic mean (which turns out to be $9.00) would be used. Note that in this example, the investor buying $1000 worth of the stock each month means buying 125 shares at $8 the first month, 111.11 shares at $9 the second month, and 100 shares at $10 in the third month. Fewer shares are purchased at higher prices while more shares are purchased at lower prices. Thus more weight is given to the lower prices than the higher prices in the calculation of the average cost per share ($8.926). If the investor had instead purchased 1000 shares each month then equal weight would be given to high and low purchase prices, leading to an average cost per share of $9.00. This explains why the harmonic mean is less than the arithmetic mean.
Sources:
http://en.wikipedia.org/wiki/Harmonic_mean
Tuesday, March 18, 2008
Weighted Geometric Mean
Formula:
Description:
I found very little information about this type of mean. So far, I've only seen it used with weights that add up to 1.
Example:
none yet
Description:
I found very little information about this type of mean. So far, I've only seen it used with weights that add up to 1.
Example:
none yet
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