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Linear Equation in One Variable

Find the valu...

Question

Find the values of n and X in each of the following cases:

(i) $\sum_{t = 1}^{n} (x_{i} - 12) = - 10$ and $\sum_{t = 1}^{n} (x_{i} - 3) = 62$

(ii) $\sum_{t = 1}^{n} (x_{i} - 10) = 30$ and $\sum_{t = 1}^{n} (x_{i} - 6) = 150$

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Solution

Ifbe the mean of the n observations, then we have

(i) The given two equations are

The equations can be rewritten as

We have to solve the above equations forand.

Subtracting the first equation from the second equation, we have

Substitute the value of n in the first equation, we have

(ii) The given two equations are

The equations can be rewritten as

We have to solve the above equations forand.

Subtracting the first equation from the second equation, we have

Substitute the value of n in the first equation, we have

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Similar questions

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

are values in a variable

x

\sum_{i = 1}^{n} (x_{i} - 2) = 110

\sum_{i = 1}^{n} (x_{i} - 5) = 20.

Find the value of

n

For observations $x_{1}, x_{2}, x_{3}, . . . . . . . . . ., x_{n},$ if $\sum_{i = 1}^{n} (x_{i} + 1)^{2} = 9 n$ and $\sum_{i = 1}^{n} (x_{i} - 1)^{2} = 5 n .$ , then standard deviation of the data is

Q. A data consists of

n

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

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

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

, then the standard deviation of this data is:

The mean deviation for n observations $x_{1}, x_{2}, . . . . x_{n}$ from their mean $¯ ¯¯¯ ¯ X$ is given by

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}

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

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

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

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