Question

The mean of 12 observations was calculated as 28. Later, it was found that one observation was wrongly recorded as 46 instead of 26, and another observation was completely omitted. If the correct mean is 27, find the value of the omitted observation.

• A. \(36\)
• B. \(18\)
• C. \(35\)
• D. \(28\)

Hint:

For corrected mean problems, always follow these three steps:
(1) Find the original (wrong) sum: Wrong Mean $\times$ Wrong $n$.
(2) Correct any wrongly recorded values by subtracting wrong entries and adding correct ones.
(3) Add the omitted value and set the new sum equal to Correct Mean $\times$ Correct $n$.
Watch carefully whether the number of observations changes (it does when an observation is omitted).

Answer 1

The Correct Option is C

Step 1: Recall the mean rule.
Mean equals the sum of observations divided by their count. So sum equals mean times count. We will adjust the sum step by step.

Step 2: Find the first reported sum.
The mean was taken as $28$ for $12$ observations, so the sum used was $28\times 12 = 336$.

Step 3: Fix the wrongly recorded value.
One value was written as $46$ but should be $26$. Remove the wrong and add the right. \[ 336 - 46 + 26 = 316 \]

Step 4: Account for the omitted value.
One observation was left out. Let it be $x$. The genuine total over all the real observations is $316$ plus this missing value $x$.

Step 5: Use the correct mean.
The correct mean is $27$. Working out the true total that makes the corrected data give a mean of $27$ leads to the equation that fixes $x$.

Step 6: Solve for the missing value.
Balancing the corrected sum against the true total gives $x = 35$. So the omitted observation is \[ \boxed{35} \]