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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?

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  1. 250
  2. 125
  3. 120
  4. Cannot be determined due to insufficient data

Answer (Detailed Solution Below)

Option 2 : 125
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Detailed Solution

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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

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