The Mean and Median of 100 Observations are 50 and 52 Respectively. The value

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The Mean and Median of 100 Observations are 50 and 52 Respectively. The value of the Largest Observation is 100. It was Later Found That it is 110 Not 100. Find the True Mean and Median.

Answer

Arithmetic Mean = ∑X/N
Given : Mean = 50 and N = 100
Therefore,
50 = ∑X/100
∑X (Wrong) = 5000
Correct value = 110
Incorrect value = 100
Correct Arithmetic Mean = {∑X (Wrong) + Correct value of observation – Incorrect value of observation }/N
⇒ Correct Mean = (5000 + 110 – 100)/100
⇒ Correct mean = 5010/100
⇒ Correct Mean = 50.1

Median will remain same i.e, median = 52

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