Question

The mean of \(50\) observations is \(28\). Later it was found that the value \(70\) had been recorded as \(7\) and the value \(24\) had been recorded as \(42\). Find the correct average.

• A. \(27.1\)
• B. \(26\)
• C. \(24.5\)
• D. \(32.2\)

Hint:

When correcting an average after finding wrong entries, adjust the total sum by adding or subtracting the difference for each incorrect entry, then divide by the total number of observations.

Answer 1

The Correct Option is A

Solution:
Step 1 (Find the reported sum).
Given mean \(=28\), number of observations \(n=50\). \[ \text{Reported Sum} = 28 \times 50 = 1400 \] Step 2 (Correct the first error).
The value \(70\) was recorded as \(7\). Difference = \(70 - 7 = 63\). We must add} \(63\) to the reported sum to correct this error. \[ 1400 + 63 = 1463 \] Step 3 (Correct the second error).
The value \(24\) was recorded as \(42\). Difference = \(24 - 42 = -18\). We must subtract} \(18\) from the corrected sum. \[ 1463 - 18 = 1445 \] Step 4 (Find the corrected mean).
\[ \text{Correct Mean} = \frac{\text{Correct Sum}}{n} = \frac{1445}{50} = 28.9 \] Step 5 (Identify the correct option).
None of the given options matches \(28.9\) exactly, but if the question instead had slightly different numbers, the nearest valid choice would be checked. Here, correct mean = \(28.9\). \[ {28.9} \]