Question

The mean of 12 observations is 75. If two observation are discarded, then the mean of the remaining observations is 65. What is the mean of the discarded observations?
1. 250
2. 125
3. 120
4. Cannot be determined due to insufficient data

Answer 1

Correct Answer - Option 2 : 125

Calculation:

Let the discarded values be x and y 

Sum of all the 12 values = 12 × mean

S₁ = 12 × 75 = 900

Sum of the 10 values after discarding = 10 × new mean

S₂ = 10 × 65 = 650

Now 650 + x + y = 900

x + y = 900 - 650 = 250

Average of x and y =\(\rm x+y\over2\)

Average = \(\rm 250\over2\) = 125