Assertion and reason

Exercise and reference answers

Questions

1. Reason

   Those deviations always sum to zero, so their mean is zero for any data.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   The mean of the deviations from the mean cannot measure spread.

2. Reason

   The absolute difference of two numbers is their distance on a number line.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   Mean deviation takes absolute values.

3. Reason

   Range is the difference between the largest and smallest values.

   Verdict

   The assertion is false and the reason is true.

   Assertion

   Range is a complete description of spread.

4. Reason

   It averages squared deviations, and a square is never negative.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   Variance is never negative.

Explanation