The observations 6, 8, x, 15, 18 are written in ascending order and their median is 11. What is the mean of the data?
Class 9StatisticsStatistics and Probability
A11
B12.4
C11.6
D58
Step-by-Step Solution
n=5 (odd), so the median is the 3rd value, giving x=11. Sum = 6 + 8 + 11 + 15 + 18 = 58, so the mean = 558=11.6. The mean and the median need not be equal.
Answer: C) 11.6
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.
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