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Mathematics

If each observation of a given set of data is increased by 5, their mean:

  1. remains the same

  2. becomes five times

  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.

New median=x1+5+x2+5+x3+53=x1+x2+x3+153=x1+x2+x33+153=x1+x2+x33+5=M+5.\text{New median}= \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 + x3}{3} + 5\\[1em] = M + 5.

Hence, option 4 is the correct option.

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