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

Standard deviation about mean $(¯ x)$ for a given discrete frequency distribution $x_{1}, x_{2}, x_{3}, . . . . . x_{n}$ with frequencies $f_{1}, f_{2}, f_{3}, . . . f_{n}$ is

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. For observations

x_{1}, x_{2}, x_{3}, . . . . . . . . . ., x_{n},

\sum_{i = 1}^{n} (x_{i} + 1)^{2} = 9 n

and

\sum_{i = 1}^{n} (x_{i} - 1)^{2} = 5 n .

, then standard deviation of the data is

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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 $σ = \sqrt{\frac{1}{n} \sum_{i = 1}^{n} (x_{i} - ¯ x)^{2}}$ .