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Mathematics

The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is

  1. 28

  2. 30

  3. 35

  4. 38

Statistics

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Answer

By formula,

Mean =Sum of observationsNo. of observations30=Sum of observations5Sum of observations=150\text{Mean } = \dfrac{\text{Sum of observations}}{\text{No. of observations}} \\[1em] 30 = \dfrac{\text{Sum of observations}}{5} \\[1em] \text{Sum of observations} = 150

Let excluded number be x.

Given, on excluding x the mean is 28.

∴150−x4=28⇒150−x=112⇒x=150−112⇒x=38.\therefore \dfrac{150 - x}{4} = 28 \\[1em] \Rightarrow 150 - x = 112 \\[1em] \Rightarrow x = 150 - 112 \\[1em] \Rightarrow x = 38.

Hence, Option 4 is the correct option.

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