Explanation of Coefficient of Variation:

The coefficient of variation (CV) is a statistical measure that represents the relative variability of a dataset. It is calculated as the ratio of the standard deviation to the mean of the dataset, expressed as a percentage.

Calculation of Coefficient of Variation:

To calculate the coefficient of variation, we need to first find the standard deviation and the mean of the dataset. The formula for the standard deviation is:

`Standard deviation = √(Σ(xi - x̄)² / n)`

where xi is the ith observation, x̄ is the mean of the dataset, and n is the total number of observations.

Once we have the standard deviation, we can calculate the coefficient of variation using the formula:

`Coefficient of variation = (Standard deviation / Mean) x 100%`

Calculation of Sum of Squared Deviations:

The sum of squared deviations is a measure of the dispersion of a dataset. It is calculated by taking the sum of the squared differences between each observation and the mean of the dataset. The formula for the sum of squared deviations is:

`Sum of squared deviations = Σ(xi - x̄)²`

where xi is the ith observation and x̄ is the mean of the dataset.

Calculation of Coefficient of Variation using Sum of Squared Deviations:

In order to calculate the coefficient of variation using the sum of squared deviations, we need to first calculate the variance using the formula:

`Variance = Sum of squared deviations / (n - 1)`

where n is the total number of observations.

Once we have the variance, we can calculate the standard deviation using the formula:

`Standard deviation = √Variance`

Finally, we can calculate the coefficient of variation using the formula:

`Coefficient of variation = (Standard deviation / Mean) x 100%`

Answer:

Since the sum of squared deviations is given, we can find the variance as:

`Variance = Sum of squared deviations / (n - 1) = 360 / (40 - 1) = 9.23`

To find the standard deviation, we take the square root of the variance:

`Standard deviation = √9.23 = 3.04`

Assuming the mean of the dataset is between 40 and 10, we can use the midpoint of the range as an estimate of the mean. The midpoint is:

`Midpoint = (40 + 10) / 2 = 25`

Using this estimate of the mean, we can calculate the coefficient of variation as:

`Coefficient of variation = (Standard deviation / Mean) x 100% = (3.04 / 25) x 100% = 12.16%`

Therefore, the coefficient of variation is 12.16%.