If the variance is 20 and each value is divided by 2, what is the new variance?

The variance of a dataset measures the dispersion of its values around the mean. When each value in the dataset is divided by a constant, the new variance is affected by the square of that constant.

In this case, if the original variance is 20 and each value is divided by 2, the new variance can be calculated using the following relationship:

New Variance = (Original Variance) × (Constant)^2

Here, the constant is 1/2 (since we are dividing by 2). Therefore:

New Variance = 20 × (1/2)^2

New Variance = 20 × (1/4)

New Variance = 20/4

New Variance = 5

Thus, when each value is divided by 2, the new variance becomes 5. This demonstrates how scaling a dataset affects its variance, specifically that the variance decreases by the square of the scaling factor.