Final answer:
The statement is false since variance should be calculated with precision and not defined by rounding. It can be reported to a specific precision after calculation.
Step-by-step explanation:
The statement 'The variance of the discrete random variable is the variance for x rounded to the nearest hundredth' is false. Variance is a measure of how much the values of a random variable vary from the mean, and it is not defined by any particular rounding whatsoever. It must be calculated with precision according to the formula for variance, which is σ² = Σ (x − μ)² P(x), where σ² represents variance, x represents values of the random variable X, μ is the mean of X, P(x) represents the probability of x, and Σ signifies the summation of the products (x-μ)² P(x) for all values.
Once the variance is found, it can be reported to the desired degree of accuracy, which might be to the nearest hundredth in some contexts, but the process of finding the variance should be carried out with as much precision as possible to avoid errors. The standard deviation of a discrete random variable, represented as σ, is the square root of the variance, and once calculated, it may be presented with a specific precision, such as rounding to the nearest hundredth for convenience or reporting standards.