The arithmetic mean of 12 observations is 15. If two observations 20 and 25 are removed then the arithmetic mean of remaining observations is

Options

A. 14.5
B. 13.5
C. 12.5
D. 13

Explanation

To solve the problem step by step, we will follow the logic outlined in the video transcript.

### Step 1: Calculate the sum of the 12 observations
The arithmetic mean (AM) is given as 15 for 12 observations. The formula for the arithmetic mean is:

\[ \text{AM} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]

From this, we can find the sum of the observations:

\[ \text{Sum of observations} = \text{AM} \times \text{Number of observations} = 15 \times 12 = 180 \]

### Step 2: Remove the two observations
We need to remove the observations 20 and 25 from the sum of the observations. Thus, we calculate the new sum:

\[ \text{New sum} = \text{Original sum} - (20 + 25) = 180 - 45 = 135 \]

### Step 3: Calculate the new number of observations
After removing the two observations, the number of observations becomes:

\[ \text{New number of observations} = 12 - 2 = 10 \]

### Step 4: Calculate the new arithmetic mean
Now we can find the new arithmetic mean using the new sum and the new number of observations:

\[ \text{New AM} = \frac{\text{New sum}}{\text{New number of observations}} = \frac{135}{10} = 13.5 \]

### Final Answer
The arithmetic mean of the remaining observations is **13.5**.

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