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NDA (Held On: 19 Apr 2015) Maths Previous Year paper

Option 4 : 38

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__Concept:__

**Mean: **It is the sum of all observations upon a number of observations.

If x_{1}, x_{2}, x_{3}, …., x_{n} are the observations, then mean is given as:

\(\bar{X'}=\frac{x_1+x_2+...+x_n}{n}\)

__Calculation:__

Given: Mean X̅ = 30

New mean be \(\bar{X'}=28\)

So, \(\bar{X'}=\frac{x_1+x_2+...+x_4}{4}\)

\(\Rightarrow 28=\frac{x_1+x_2+...+x_4}{4}\)

⇒112 = x_{1} + x_{2} + ⋯ + x_{4}

Now, \(\bar{X}=\frac{x_1+x_2+...+x_5}{5}\)

\(\Rightarrow 30=\frac{x_1+x_2+...+x_5}{5}\)

⇒ 150 = x_{1} + x_{2} + ⋯ + x_{5}

⇒ 150 = 112 + x_{5}

⇒ 38 = x_{5}

The excluded number is 38.