The mean of 100 observations was calculated as 40. It was found later on that one of the observations was misread as 83 instead of 53 The correct mean is

Options

A. 39.7
B. 112.2
C. 21.32
D. 44.32

Answer

To find the correct mean after identifying the misread observation, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the Total Sum of Observations:**
The mean of the 100 observations is given as 40. To find the total sum of these observations, we multiply the mean by the number of observations.
\[ \text{Total Sum} = \text{Mean} \times \text{Number of Observations} = 40 \times 100 = 4000 \]

2. **Identify the Error in the Misread Observation:**
One observation was misread as 83 instead of 53. We need to find the difference between the misread value and the correct value.
\[ \text{Error} = \text{Misread Value} - \text{Correct Value} = 83 - 53 = 30 \]

3. **Adjust the Total Sum:**
Since the misread value is greater than the correct value, we need to subtract the error from the total sum to get the correct total sum.
\[ \text{Correct Total Sum} = \text{Total Sum} - \text{Error} = 4000 - 30 = 3970 \]

4. **Calculate the Correct Mean:**
Now, we can find the correct mean by dividing the corrected total sum by the number of observations.
\[ \text{Correct Mean} = \frac{\text{Correct Total Sum}}{\text{Number of Observations}} = \frac{3970}{100} = 39.7 \]

### Final Answer:
The correct mean is **39.7**.

---