Shortcut Trick
Arrange the 15 data points in Ascending Order: 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 4, 5, 5, 5.
Since the total number of observations (n = 15) is Odd, the Median is the exact middle term.
Middle Position = (n + 1) ÷ 2 = (15 + 1) ÷ 2 = 8th position.
The value at the 8th position in the sorted list is 2.
∴ The correct answer is 2.
Alternate Method
Given Data: 0, 3, 2, 1, 5, 3, 4, 5, 5, 2, 2, 0, 0, 1, 2
⇒ Step 1: Count total number of observations (n). Here, n = 15.
⇒ Step 2: Arrange data in Ascending Order: 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 4, 5, 5, 5.
⇒ Step 3: Apply Median Formula for odd n: Median = ((n + 1) ÷ 2)th term.
⇒ Step 4: Median = ((15 + 1) ÷ 2)th term = 8th term.
⇒ Step 5: Identifying the 8th term from the sorted list: 2.
∴ The correct answer is 2.
Additional Information
Median for Even Number of Observations
If n is even, the median is the average of the (n ÷ 2)th term and the ((n ÷ 2) + 1)th term.
Mode of Data
The Mode is the value that appears most frequently. In this data set, 2 appears 4 times, so the Mode is also 2.
Mean of Data
The Arithmetic Mean is the sum of all observations divided by the total number of observations.