14 observations are 10, 11, 11, 12, 13, 14, 12, 13, 10, 12, 12, 14, 14 and 15. What is the median of the given observations?

Options

A. 12
B. 13
C. 14
D. 10

Answer

To find the median of the given observations, we will follow these steps:

### Step 1: List the Observations
The observations provided are:
10, 11, 11, 12, 13, 14, 12, 13, 10, 12, 12, 14, 14, 15

### Step 2: Sort the Observations in Ascending Order
We need to arrange the observations in ascending order:
10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 14, 15

### Step 3: Determine the Number of Observations
Count the number of observations:
There are 14 observations.

### Step 4: Identify the Median Position
Since the number of observations (n) is even (n = 14), the median will be the average of the two middle values. The positions of the two middle values can be found using the formula:
- Middle positions = n/2 and (n/2) + 1
- For n = 14, the middle positions are 14/2 = 7 and (14/2) + 1 = 8.

### Step 5: Find the Two Middle Values
From the sorted list:
- The 7th observation is 12.
- The 8th observation is also 12.

### Step 6: Calculate the Median
Now, we calculate the median by taking the average of the two middle values:
Median = (12 + 12) / 2 = 24 / 2 = 12.

### Final Answer
The median of the given observations is **12**.

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