The mean of `40` numbers was found to be `38`. Later on, it was detected that a number `56` was misread as `36`. find the correct mean of the given numbers.

Options

A. `40.5`
B. `38.5`
C. `34.5`
D. `48.5`

Explanation

To find the correct mean of the given numbers after correcting the misread value, we can follow these steps:

### Step 1: Calculate the original sum of the numbers.
The mean of the 40 numbers is given as 38. The formula for mean is:

\[ \text{Mean} = \frac{\text{Sum of numbers}}{\text{Count of numbers}} \]

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

\[ \text{Sum of numbers} = \text{Mean} \times \text{Count of numbers} = 38 \times 40 = 1520 \]

### Step 2: Identify the misread number and the correct number.
It is stated that the number 56 was misread as 36.

- Misread number = 36
- Correct number = 56

### Step 3: Adjust the sum to correct the misread value.
To find the correct sum, we need to subtract the misread number and add the correct number to the original sum:

\[ \text{Correct Sum} = \text{Original Sum} - \text{Misread Number} + \text{Correct Number} \]

Substituting the values we have:

\[ \text{Correct Sum} = 1520 - 36 + 56 \]

Calculating this:

\[ \text{Correct Sum} = 1520 - 36 + 56 = 1520 - 36 + 56 = 1540 \]

### Step 4: Calculate the correct mean.
Now that we have the correct sum, we can find the correct mean using the same formula:

\[ \text{Correct Mean} = \frac{\text{Correct Sum}}{\text{Count of numbers}} = \frac{1540}{40} \]

Calculating this gives:

\[ \text{Correct Mean} = 38.5 \]

### Final Answer:
The correct mean of the given numbers is **38.5**.

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