The mean of the marks scored by 40 students was found to be 35. Later on it was discovered that a score of 43 was misread as 34. The correct mean is

Options

A. 35.2
B. 39.4
C. 39.8
D. 39.2

Answer

To find the correct mean after the misreading of a score, we can follow these steps:

### Step 1: Calculate the initial total sum of marks
The mean of the marks scored by 40 students was found to be 35. The formula for mean is:

\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Total number of observations}} \]

Given that the mean is 35 and the total number of students is 40, we can find the sum of the marks:

\[ \text{Sum of marks} = \text{Mean} \times \text{Total number of observations} = 35 \times 40 = 1400 \]

### Step 2: Identify the error in the sum
It was discovered that a score of 43 was misread as 34. This means that the sum of marks calculated (1400) included the incorrect score of 34 instead of the correct score of 43.

To correct this, we need to adjust the sum:

1. Subtract the incorrect score (34) from the total sum.
2. Add the correct score (43) to the total sum.

So, the corrected sum will be:

\[ \text{Corrected Sum} = 1400 - 34 + 43 \]

Calculating this gives:

\[ \text{Corrected Sum} = 1400 - 34 + 43 = 1400 - 34 + 43 = 1409 \]

### Step 3: Calculate the new mean
Now that we have the corrected sum, we can find the new mean using the same formula for mean:

\[ \text{New Mean} = \frac{\text{Corrected Sum}}{\text{Total number of observations}} = \frac{1409}{40} \]

Calculating this gives:

\[ \text{New Mean} = 35.225 \]

### Step 4: Round the mean (if necessary)
In many cases, we round the mean to two decimal places, so:

\[ \text{New Mean} \approx 35.23 \]

Thus, the correct mean is approximately **35.23**.