Question

The mean of \(10\) observations was calculated as \(40\). It was detected on rechecking that the value of one observation \(45\) was wrongly copied as \(15\). Find the correct mean.

• A. \(43\)
• B. \(34\)
• C. \(40\)
• D. \(60\)

Hint:

Remember:

• \[ \text{Mean} = \frac{\text{Sum}}{n} \]
• If an observation is misread: \[ \text{Correct Sum} = \text{Wrong Sum} + (\text{Correct value} - \text{Wrong value}) \]

Answer 1

The Correct Option is A

Concept: Mean is given by: \[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \] If one observation is wrongly recorded, first correct the total sum and then calculate the corrected mean.

Step 1: Calculate the incorrect total sum. Given: \[ \text{Mean} = 40 \] Number of observations: \[ n = 10 \] Thus: \[ \text{Incorrect sum} = 40 \times 10 \] \[ = 400 \]

Step 2: Correct the wrongly copied observation. Actual observation: \[ 45 \] Wrongly copied as: \[ 15 \] Difference: \[ 45-15 = 30 \] Correct sum: \[ 400 + 30 \] \[ = 430 \]

Step 3: Calculate the correct mean. \[ \text{Correct mean} = \frac{430}{10} \] \[ = 43 \] Therefore, \[ \boxed{43} \]