<p>The mean of the data set comprising of 16 observations is 16. If one of the observation valued 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</p>
Step-by-Step Solution
Key Concept: When modifying a dataset, calculate the sum using mean × count, then adjust by subtracting deleted values and adding new values, finally divide by the new count to find the new mean.
<p><strong>Step 1:</strong> Find the original sum of 16 observations.</p><p>Mean = 16, n = 16</p><p>Sum = Mean × n = 16 × 16 = 256</p><p><strong>Step 2:</strong> Delete one observation valued 16 and add three new observations (3, 4, 5).</p><p>New Sum = 256 - 16 + 3 + 4 + 5 = 256 - 16 + 12 = 252</p><p><strong>Step 3:</strong> Calculate new mean with new number of observations.</p><p>New n = 16 - 1 + 3 = 18</p><p>New Mean = 252/18 = 14</p><p>∴ Answer: D (14)</p>
Correct Answer: D