The mean of a data set comprising of 16 observations is 16. If one of the observation value 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data is

The mean of the original data set with 16 observations is given as 16. The mean is calculated as the sum of all observations divided by the number of observations. Therefore, the sum of the original 16 observations can be found by multiplying the mean by the number of observations.

So, original sum $$ S = 16 \times 16 = 256 $$.

One observation with the value 16 is deleted. Subtract this value from the original sum: $$ S_{\text{after deletion}} = 256 - 16 = 240 $$. After deletion, the number of observations becomes $$ 16 - 1 = 15 $$.

Next, three new observations valued 3, 4, and 5 are added. Add these values to the sum: $$ S_{\text{new}} = 240 + 3 + 4 + 5 = 240 + 12 = 252 $$. After adding these observations, the total number of observations becomes $$ 15 + 3 = 18 $$.

The mean of the resultant data is the new sum divided by the new number of observations: $$ \text{New mean} = \frac{252}{18} $$.

Simplify the division: $$ 252 \div 18 = 14 $$, since $$ 18 \times 14 = 252 $$.

Thus, the mean of the resultant data is 14.0.

Comparing with the options, A is 14.0, B is 16.8, C is 16.0, and D is 15.8. Hence, the correct answer is Option A.