Standard deviation for x 1- x 2- - x n about mean can be expressed as -1- n - i -1 n x i - x 2-A- FalseB- True

The correct option is B True We know variance also expressed as σ^2=1/n∑_i=1^n(x_i x̅)^2 we call standard deviation as the square roof of variance (σ^2). There ...

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Standard XI

Mathematics

Standard Deviation about Mean

Standard devi...

Question

Standard deviation for $x_{1}, x_{2}, . . . . . x_{n}$ about mean can be expressed as $\sqrt{\frac{1}{n} \sum_{i = 1}^{n} (x_{i} - ¯ x)^{2}}$ .

True

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False

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Solution

The correct option is A
True

We know variance also expressed as $σ^{2} = \frac{1}{n} \sum_{i = 1}^{n} (x_{i} - ¯ x)^{2}$ we call standard deviation as the square roof of variance $(σ^{2})$ . Therefore $σ = \sqrt{\frac{1}{n} \sum_{i = 1}^{n} (x_{i} - ¯ x)^{2}}$ .

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Similar questions

Standard deviation for $x_{1}, x_{2}, . . . . . x_{n}$ about mean can be expressed as $\sqrt{\frac{1}{n} \sum_{i = 1}^{n} (x_{i} - ¯ x)^{2}}$ .

Q. Let

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

be n observations and

X

be their arithmetic mean. The standard deviation is given by

(a)

\sum_{i = 1}^{n} {(x_{i} - X)}^{2}

(b)

\frac{1}{n} \sum_{i = 1}^{n} {(x_{i} - X)}^{2}

(c)

\sqrt{\frac{1}{n} \sum_{i = 1}^{n} {(x_{i} - X)}^{2}}

(d)

\sqrt{\frac{1}{n} \sum_{i = 1}^{n} x_{i}^{2} - X^{2}}

Q. The mean deviation for n observations

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

from their mean

X

is given by

(a)

\sum_{i = 1}^{n} (x_{i} - X)

(b)

\frac{1}{n} \sum_{i = 1}^{n} (x_{i} - X)

(c)

\sum_{i = 1}^{n} {(x_{i} - X)}^{2}

(d)

\frac{1}{n} \sum_{i = 1}^{n} {(x_{i} - X)}^{2}

Q. If

n \sum i = 1 (x_{i} - a)

and

n \sum i = 1 (x_{i} - a)^{2} = n a, (n, a > 1)

then the standard deviation of

n

observations

x_{1}, x_{2}, \dots, x_{n}

is :

Q. Given n observations x₁, x₂ ......x_n and their central tendency a, the mean deviation about a, M.D(a) =

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Standard deviation for x1,x2,.....xn about mean can be expressed as √1n∑ni=1(xi−¯x)2.

The correct option is A True We know variance also expressed as σ2=1n∑ni=1(xi−¯x)2 we call standard deviation as the square roof of variance (σ2). Therefore σ=√1n∑ni=1(xi−¯x)2.

Standard deviation for $x_{1}, x_{2}, . . . . . x_{n}$ about mean can be expressed as $\sqrt{\frac{1}{n} \sum_{i = 1}^{n} (x_{i} - ¯ x)^{2}}$ .

The correct option is A
True

We know variance also expressed as $σ^{2} = \frac{1}{n} \sum_{i = 1}^{n} (x_{i} - ¯ x)^{2}$ we call standard deviation as the square roof of variance $(σ^{2})$ . Therefore $σ = \sqrt{\frac{1}{n} \sum_{i = 1}^{n} (x_{i} - ¯ x)^{2}}$ .