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6.5.A SKEWNESS

Skewness measures asymmetry around the mean. The parameter is best

interpreted as relative to the Normal Density Function (whose Skewness

equals zero). The interpretation of the Skewness for a series (relative to

the Normal Density Function) is:

вЂ” Skewness > 0 asymmetric tail with more values above the mean.

вЂ” Skewness < 0 asymmetric tail with more values below the mean.

The next three figures shown Density Functions that have a Skewness >

0, = 0, and < 0, respectively, for three variables Y1, Y2 and Y3. (Y2 is

distributed Normally).

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Statistical Analysis with Excel

Figure 96: Distribution of series Y1.

Skewness > 0

Figure 97: Distribution of series Y2.

Skewness = 0.

Figure 98: Distribution of series Y3

Skewness < 0

Samples will be available at http://www.vjbooks.net/excel/samples.htm.

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Chapter 6: Functions for Basic Statistics

Figure 99: SKEW (Skewness)

Menu path to function: INSERT / FUNCTION / STATISTICAL / SKEW

6.5.B KURTOSIS

Compared with the Normal Density Function (which has a Kurtosis of

zero), the interpretation of the kurtosis for a series is:

вЂ” Kurtosis > 0 peaked relative to the Normal Density Function

вЂ” Kurtosis < 0 flat relative to the Normal Density Function

The next figure shows three Density Functions. The Density Functions

lie around the same Mean and Median, but note the difference in the

relative flatness of the Density Functions:

Distribution of series X1 is the flattest with a Kurtosis < 0, that of X2 is

less flat with a Kurtosis = 0 (a Normal Density Function) and that of

series X3 is the least flat with a Kurtosis > 0.

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Statistical Analysis with Excel

Figure 100: Example of Density Functions with different Skewness

Samples will be available at http://www.vjbooks.net/excel/samples.htm.

Menu path to function: INSERT / FUNCTION / STATISTICAL / KURT

FUNCTIONS ENDING WITH AN вЂњAвЂќ SUFFIX

6.6

These functions calculates the same statistic as their вЂњtwinвЂќ formula (the

one without the prefix вЂњAвЂќ) but include a wider range of valid cell values

in the relevant formula. The вЂњAвЂќ вЂ“suffixed functions include the following

types of cell values:

вЂ” Logical (and not numeric) like вЂњTrueвЂќ and вЂњFalseвЂќ (valued as 1 and 0,

respectively),

вЂ” Blank cells (valued as 0), and

вЂ” Text (valued as 0).

A text string or a blank cell is valued as zero. The next table lists these

twin functions:

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Chapter 6: Functions for Basic Statistics

Table 13: Functions ending with the вЂњAвЂќ suffix.

The nonвЂ“

The вЂњAвЂќ prefixed

prefixed Comment

вЂњtwinвЂќ formula

function

AVERAGEA

AVERAGE Simple average/mean

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