Find the median of: 33, 27, 41, 39, 25, 30.

Class 9StatisticsStatistics and Probability

Step-by-Step Solution

Arrange first: 25, 27, 30, 33, 39, 41.

n = 6

(even), so the median =

\frac{30 + 33}{2} = 31.5

. Averaging the middle two of the unsorted list gives

\frac{41 + 39}{2} = 40

, which is the classic mistake.

Answer: D) 31.5

**Step 1**: Arrange data in ascending order.
**Step 2**: Count items (n).
**Step

3 a

**: If

n

is ODD, median is the value at position

(n + 1) /2

.
**Step

3 b

**: 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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