The average of 100 numbers is 60. One observation 80 is removed and another number x is added such that the average decreases by 0.5. Find x?
Explanation:
Mean of 100 observations = 60
Correction to be made = x – 80
New average, 60×100 + (x - 80)100 = 59.5
⇒ 6000 + x – 80 = 5950
⇒ x = 30.
Alternately,
Since the average of 100 numbers decreases by 0.5, the sum decreases by 100 × 0.5 = 50.
Hence the number added is 50 less than the number removed
⇒ 50 = number removed – number added = 80 – x.
Hence, option (c).
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