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Mathematics

If each observation of the data is increased by 5, then their mean

  1. remains the same

  2. becomes 5 times the original mean

  3. is decreased by 5

  4. is increased by 5

Statistics

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Answer

Let x1, x2, x3 be the observations.

So, their mean (M) = x1+x2+x33\dfrac{x1 + x2 + x_3}{3}

Since, each observations is increased by 5, so observations will be

x1 + 5, x2 + 5, x3 + 5.

Mean (M1)=x1+5+x2+5+x3+53=x1+x2+x3+153=x1+x2+x33+153=x1+x2+x33+5.\text{Mean (M}1) = \dfrac{x1 + 5 + x2 + 5 + x3 + 5}{3} \\[1em] = \dfrac{x1 + x2 + x3 + 15}{3} \\[1em] = \dfrac{x1 + x2 + x3}{3} + \dfrac{15}{3} \\[1em] = \dfrac{x1 + x2 + x_3}{3} + 5.

So, M1 = M + 5.

Hence, Option 4 is the correct option.

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