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Let $\underset{̲}{x}$ be the mean of $x_{1}, x_{2}, . . ., x_{n}$ and $\underset{̲}{y}$ the mean of $y_{1}, y_{2}, . . ., y_{n}$ . If $\underset{̲}{z}$ is the mean of $x_{1}, x_{2}, . . ., x_{n}$ , $y_{1}, y_{2}, . . ., y_{n}$ , then determine the value of $\underset{̲}{z}$ ?

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\underset{̲}{x} + \underset{̲}{y}

\frac{\underset{̲}{x} + \underset{̲}{y}}{2}

\frac{\underset{̲}{x} + \underset{̲}{y}}{n}

\frac{\underset{̲}{x} + \underset{̲}{y}}{2 n}

answer is B.

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Detailed Solution

Given,

\underset{̲}{x}

is the mean of

x_{1}, x_{2}, . . ., x_{n}

\underset{̲}{y}

is the mean of

y_{1}, y_{2}, . . ., y_{n}

and

\underset{̲}{z}

is the mean of

x_{1}, x_{2}, . . ., x_{n}

y_{1}, y_{2}, . . ., y_{n}

.
We know that the mean of given numbers is the average of the given numbers.

\Rightarrow

\underset{̲}{x} = \frac{x_{1} + x_{2} + . . . + x_{n}}{n}

\Rightarrow \underset{̲}{x} n = x_{1} + x_{2} + . . . . . + x_{n}

Also,

\underset{̲}{y} = \frac{y_{1} + y_{2} + . . . + y_{n}}{n}

\Rightarrow \underset{̲}{y} n = y_{1} + y_{2} + . . . . . + y_{n}

\underset{̲}{z}

is the mean of

x_{1}, x_{2}, . . ., x_{n}

y_{1}, y_{2}, . . ., y_{n}

… (given).

\Rightarrow \underset{̲}{z}

\frac{x_{1} + x_{2} + . . . + x_{n} + y_{1} + y_{2} + . . . + y_{n}}{2 n}

\Rightarrow \underset{̲}{z} = \frac{\underset{̲}{x} n + \underset{̲}{y} n}{2 n}

\Rightarrow \underset{̲}{z}

\frac{\underset{̲}{x} + \underset{̲}{y}}{2}

Hence, option

2

is correct.

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Let x̲ be the mean of x1,x2,...,xnand y̲ the mean of y1,y2,...,yn. If z̲ is the mean of x1,x2,...,xn, y1,y2,...,yn, then determine the value of z̲?

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Let $\underset{̲}{x}$ be the mean of $x_{1}, x_{2}, . . ., x_{n}$ and $\underset{̲}{y}$ the mean of $y_{1}, y_{2}, . . ., y_{n}$ . If $\underset{̲}{z}$ is the mean of $x_{1}, x_{2}, . . ., x_{n}$ , $y_{1}, y_{2}, . . ., y_{n}$ , then determine the value of $\underset{̲}{z}$ ?