Final answer:
Replacing two observations in a set with the same mean does not alter the overall mean if the sum of the replacements equals the sum of the original observations, thus the new mean remains 15.
Step-by-step explanation:
The mean of twenty observations is given as 15. Replacing two observations, 3 and 14, with 8 and 9 respectively, affects the overall mean slightly. To find the new mean, we can calculate the change in sum caused by the replacement. The initial sum for all twenty observations is 20 × 15 (since mean = sum/number of observations). When replacing 3 and 14 with 8 and 9, the sum of observations increases by (8 - 3) + (9 - 14) = 5 + (-5) = 0. Since the total sum does not change, the new mean remains the same, which is 15.