CMA Study Group

There was no attachment to review.  Here's an example.

To calculate the Mean:

Possible Sales Value (V)                          Probability of Occurrence (P)                V x P

$600                                                       .05                                                          30

$800                                                       .10                                                          80

$1000                                                    .70                                                          700

$1200                                                    .10                                                          120

$1400                                                    .05                                                          70

                                                                ∑ = 1.00                                           ∑= 1000 = µ

Each possible sales value is multiplied by its respective probability.  The probability values may be based on trends, industry ratios, experience, or other sources of information.  We add together the products (VxP) to find the mean of the possible sales distribution.  The mean of sale forecast distribution is $1000. 

To calculate the Standard Deviation:

Possible Sales    Probability of

Value (V)             Occurrence (P)                  V - µ                       (V - µ)²                  P (V - µ)²

$600                       .05                                -400                       160,000                 8,000

$800                       .10                                -200                       40,000                   4,000

$1000                    .70                                   0                           0                            0

$1200                    .10                                   200                       40,000                   4,000

$1400                    .05                                   400                       160,000                  8,000

                                                                                                                                ∑ = 24,000

                                                                                                                              SQRT 24,000 = 155 = δ

To calculate the SD of sales distribution, we subtract the mean from each possible sales value, square that difference, and then multiply by the probability of that sales outcome.  These differences squared, times their respective probabilities, are then added together, and the square root of this number is taken.  The result is the standard deviation of the distribution of possible sales values.  The SD result is 155, and severs as the measure of the degree of risk present in sales forecast distribution.

Whenever we want to compare risk of investments that have different means, we use the coefficient of variation.  To compare the degree of risk among distributions of different sizes, we should use a statistic that measures relative riskiness.  The coefficient of variation (CV) measures relative risk by relating the SD to the mean.

CV = Standard Deviation / Mean

155 / 1000 = .155 or 15.5%

The CV provides a standardized measure of the degree of risk that can be used to compare alternatives.  We use the CV instead of the SD to compare distributions that have means with different values because CV adjusts for the difference, whereas the SD does not.

There was no attachment to review.  Here's an example.

To calculate the Mean:

Possible Sales Value (V)                          Probability of Occurrence (P)                V x P

$600                                                       .05                                                          30

$800                                                       .10                                                          80

$1000                                                    .70                                                          700

$1200                                                    .10                                                          120

$1400                                                    .05                                                          70

                                                                ∑ = 1.00                                           ∑= 1000 = µ

Each possible sales value is multiplied by its respective probability.  The probability values may be based on trends, industry ratios, experience, or other sources of information.  We add together the products (VxP) to find the mean of the possible sales distribution.  The mean of sale forecast distribution is $1000. 

To calculate the Standard Deviation:

Possible Sales    Probability of

Value (V)             Occurrence (P)                  V - µ                       (V - µ)²                  P (V - µ)²

$600                       .05                                -400                       160,000                 8,000

$800                       .10                                -200                       40,000                   4,000

$1000                    .70                                   0                           0                            0

$1200                    .10                                   200                       40,000                   4,000

$1400                    .05                                   400                       160,000                  8,000

                                                                                                                                ∑ = 24,000

                                                                                                                              SQRT 24,000 = 155 = δ

To calculate the SD of sales distribution, we subtract the mean from each possible sales value, square that difference, and then multiply by the probability of that sales outcome.  These differences squared, times their respective probabilities, are then added together, and the square root of this number is taken.  The result is the standard deviation of the distribution of possible sales values.  The SD result is 155, and severs as the measure of the degree of risk present in sales forecast distribution.

There was no attachment to review.  Here's an example.

To calculate the Mean:

Possible Sales Value (V)                          Probability of Occurrence (P)                V x P

$600                                                       .05                                                          30

$800                                                       .10                                                          80

$1000                                                    .70                                                          700

$1200                                                    .10                                                          120

$1400                                                    .05                                                          70

                                                                ∑ = 1.00                                           ∑= 1000 = µ

Each possible sales value is multiplied by its respective probability.  The probability values may be based on trends, industry ratios, experience, or other sources of information.  We add together the products (VxP) to find the mean of the possible sales distribution.  The mean of sale forecast distribution is $1000. 

To calculate the Standard Deviation:

Possible Sales    Probability of

Value (V)             Occurrence (P)                  V - µ                       (V - µ)²                  P (V - µ)²

$600                       .05                                -400                       160,000                 8,000

$800                       .10                                -200                       40,000                   4,000

$1000                    .70                                   0                           0                            0

$1200                    .10                                   200                       40,000                   4,000

$1400                    .05                                   400                       160,000                  8,000

                                                                                                                                ∑ = 24,000

                                                                                                                              SQRT 24,000 = 155 = δ

To calculate the SD of sales distribution, we subtract the mean from each possible sales value, square that difference, and then multiply by the probability of that sales outcome.  These differences squared, times their respective probabilities, are then added together, and the square root of this number is taken.  The result is the standard deviation of the distribution of possible sales values.  The SD result is 155, and severs as the measure of the degree of risk present in sales forecast distribution.