From a series of 50 observations, an observation with the value of 45 is dropped, but the mean remains the same . What was the mean of 50 observations ?

Options

A. 50
B. 49
C. 45
D. 40

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step-by-Step Solution:

1. **Understanding the Problem**: We have a series of 50 observations, and when one observation (45) is dropped, the mean remains unchanged. We need to find the mean of the original 50 observations.

2. **Let the Mean be M**: We denote the mean of the 50 observations as \( M \).

3. **Formula for Mean**: The formula for the mean is given by:
\[ \text{Mean} (M) = \frac{\text{Sum of Observations}}{\text{Number of Observations}} \]

4. **Sum of Observations**: Let the sum of the 50 observations be \( S \). Therefore, we can express the mean as:
\[ M = \frac{S}{50} \]
This implies:
\[ S = 50M \]

5. **Including the Dropped Observation**: Since one observation (45) is dropped, the sum of the remaining observations (49) will be:
\[ S - 45 = 50M - 45 \]

6. **Mean of Remaining Observations**: The mean of the remaining 49 observations will still be \( M \), so we can write:
\[ M = \frac{S - 45}{49} \]
Substituting \( S \) gives:
\[ M = \frac{50M - 45}{49} \]

7. **Setting Up the Equation**: Now we can set up the equation:
\[ 49M = 50M - 45 \]

8. **Solving for M**: Rearranging the equation gives:
\[ 50M - 49M = 45 \]
Thus,
\[ M = 45 \]

9. **Conclusion**: The mean of the original 50 observations is \( 45 \).

### Final Answer:
The mean of the 50 observations is **45**.