The arithmetic mean of a set of observations is X. If each observation is divided by R and then is increased by 10, then the mean of the new series is

The arithmetic mean of a set of observations is X. If each observation is divided by R and then is increased by 10, then the mean of the new series is

  1. A

    X¯α

  2. B

    X¯+10α

  3. C

    X¯+10αα

  4. D

    αX¯+10

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    Solution:

    Let x1,x2,,xn be n observations. Then

    X¯=1nxi

    Let yi=xiα+10 Then

    1ni=1nyi=1α1ni=1nxi+1n(10n) Y¯=1αX¯+10=X¯+10αα

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