Question:
<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>
<p>16.0</p>
<p>15.8</p>
<p>14.0</p>
<p>16.8</p>
Step-by-Step Solution
Key Concept: When deleting one observation and adding three new ones, the total number of observations changes from 16 to 18. Use the relationship: new mean = (old sum - deleted value + sum of added values) / new count.
<p><strong>Step 1:</strong> Find the sum of original 16 observations.</p><p>Mean = 16, n = 16</p><p>Sum of original data = Mean × n = 16 × 16 = 256</p><p><strong>Step 2:</strong> Calculate new sum after deletion and addition.</p><p>Delete observation valued 16: Sum = 256 - 16 = 240</p><p>Add observations 3, 4, 5: Sum = 240 + 3 + 4 + 5 = 252</p><p><strong>Step 3:</strong> Find the new count of observations.</p><p>Original count: 16</p><p>After deleting 1: 15</p><p>After adding 3: 15 + 3 = 18</p><p><strong>Step 4:</strong> Calculate the new mean.</p><p>New mean = 252/18 = 14</p><p>∴ Answer: C (14)</p>
Correct Answer: C