Calculation of the average of the series

Given, variance (σ²) = 16 and coefficient of variance (CV) = 20

Calculation of standard deviation (σ)

We know that CV = (σ / mean) × 100

Therefore, σ = (CV / 100) × mean

Putting the given values, we get:

16 = σ²

20 = (σ / mean) × 100

σ = 4

Calculation of mean

We know that variance (σ²) = [(sum of squares of deviations from mean) / number of observations]

Therefore, 16 = [(sum of squares of deviations from mean) / number of observations]

Also, we know that standard deviation (σ) = root of variance (σ²)

Therefore, σ = root of 16

σ = 4

Now, we can use the formula:

σ = root of [(sum of squares of deviations from mean) / number of observations]

4 = root of [(sum of squares of deviations from mean) / number of observations]

Squaring both sides, we get:

16 = (sum of squares of deviations from mean) / number of observations

Multiplying both sides by number of observations, we get:

16 × number of observations = sum of squares of deviations from mean

Assuming the number of observations to be 'n', we get:

16n = sum of squares of deviations from mean

Conclusion

We have two equations:

σ = (CV / 100) × mean

16n = sum of squares of deviations from mean

We can solve these two equations simultaneously to get the value of mean. However, we need one more equation to solve for mean.

Hence, we cannot calculate the average of the series with the given information.