For this problem, what is the most appropriate unit for the variance for the number of friend requests? (Select the best answer.)

Question

BlackTom AI · Accepted Answer

To begin, consider what the variable represents: the number of friend requests. The unit of a single observation is 'requests'. When we compute variance, we are measuring the average of the squared deviations from the mean, which introduces squaring of the unit.

Option 1: 'no unit' would be incorrect because variance involves squaring a quantity that has units, so it cannot be dimensionless.

Option 2: 'square root of requests' would correspond to the standard deviation, not the variance. The square root operation is applied to the variance to obtain the standard deviation, so this is not the right unit for variance itself.

Option 3: 'none of the above' would be plausible only if none of the listed units matched, but there is a correct option among them.

Option 4: 'requests' would be the unit of the original data, not the variance, since variance is about squared deviations.

Option 5: 'requests squared' correctly reflects that variance has units of (unit)^2, i.e., (requests)^2. This matches the mathematical definition Var(X) = E[(X - μ)^2], where X has unit 'requests', so Var(X) has unit 'requests squared'.

Option 6: 'double requests' would imply a unit of 2 × requests, which is not meaningful for variance and does not correspond to the algebraic form of squared deviations.

In summary, the variance inherits the squared unit of the original measurement, so the appropriate unit for the variance of the number of friend requests is 'requests squared'.

For this problem, what is the most appropriate unit for the variance for the number of friend requests? (Select the best answer.)单项选择题

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