- ABoth the mean and the median become 13
- BThe mean becomes 13 but the median stays 7
- CThe median becomes 13 but the mean stays 7
- DNeither the mean nor the median changes
Step-by-Step Solution
New sum = 5 + 6 + 7 + 8 + 39 = 65, so the mean rises to 565=13. The ordered data is 5, 6, 7, 8, 39 and the 3rd value is still 7, so the median is unchanged. This is why the median is preferred when a data set has an extreme value.
Answer: B) The mean becomes 13 but the median stays 7
Key idea: Median — the middle value
**Step 1**: Arrange data in ascending order.
**Step 2**: Count items (n).
**Step 3a**: If n is ODD, median is the value at position (n+1)/2.
**Step 3b**: If n is EVEN, median is the average of values at positions n/2 and (n/2+1).
**Example odd n∗∗:3,5,7,9,11.n=5. Position (5+1)/2=3. Median = 7.
**Example even n∗∗:4,6,8,10.n=4. Positions 2 and 3 → values 6 and 8 → median = (6+8)/2=7.
Median is the right choice when there are extreme outliers, since it's not pulled by them like the mean is.