The average of 100 numbers is 60. One observation 50 is removed and another number x is added such that the average increases by 1. Find x?
Explanation:
Mean of 100 observations = 60
Correction to be made = x – 50
New average, 60×100 + (x - 50)100 = 61
⇒ 6000 + x – 50 = 6100
⇒ x = 150.
Alternately,
Since the average of 100 numbers increases by 1, the sum increases by 100 × 1 = 100.
Hence the number added is 100 more than the number removed
⇒ 100 = number added – number removed = x - 50
Hence, 150.
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