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Question

While dividing each entry in a data by a non zero number a the arithmetic mean of the new data

A
is multiplied by a
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B
does not change
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C
is divided by a
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D
is diminished by a
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Solution

The correct option is C is divided by a
Let x1,x2,x3,...,xn be n items.
Then their arithmetic mean is
¯x=x1+x2+x3+...+xnn
After dividing each entries with 'a', the items becomes
x1a,x2a,x3a,...,xna
Then their arithmetic mean is
A.M=x1a+x2a+x3a+...+xnan
=1a(x1+x2+x3+...+xnn)
=1a(¯x)
Therefore on dividing each entry by 'a' the AM means is also divided by a
Option C is correct.

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