Mean of 50 observations was found to be 80.4. But later on, it was discovered that 96 was misread as 69 at one place. Find the correct mean.

Options

A. `80.94`
B. `85`
C. `90`
D. None

Explanation

To find the correct mean after discovering the misreading of one observation, we can follow these steps:

### Step 1: Calculate the total sum of the original observations
Given that the mean of 50 observations is 80.4, we can calculate the total sum of these observations.

\[ \text{Total Sum} = \text{Mean} \times \text{Number of Observations} = 80.4 \times 50 \]

Calculating this gives:

\[ \text{Total Sum} = 4020 \]

### Step 2: Adjust the total sum for the misread observation
We need to adjust the total sum by removing the misread value (69) and adding the correct value (96).

\[ \text{Corrected Total Sum} = \text{Total Sum} - \text{Misread Value} + \text{Correct Value} \]

Substituting the values we have:

\[ \text{Corrected Total Sum} = 4020 - 69 + 96 \]

Calculating this gives:

\[ \text{Corrected Total Sum} = 4020 - 69 + 96 = 4020 - 69 + 96 = 4047 \]

### Step 3: Calculate the correct mean
Now, we can find the correct mean using the corrected total sum.

\[ \text{Correct Mean} = \frac{\text{Corrected Total Sum}}{\text{Number of Observations}} = \frac{4047}{50} \]

Calculating this gives:

\[ \text{Correct Mean} = 80.94 \]

Thus, the correct mean after adjusting for the misread observation is **80.94**.

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