If the arithmetic mean of the numbers $x_1, x_2, x_3, ..., x_n$ is $\bar{x}$,then the arithmetic mean of the numbers $ax_1 + b, ax_2 + b, ax_3 + b, ..., ax_n + b$,where $a$ and $b$ are two constants,would be:
- A$\bar{x}$
- B$n a \bar{x} + nb$
- C$a \bar{x}$
- D$a \bar{x} + b$
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Similar Questions
Consider a set of observations ${x_1}, {x_2}, {x_3}, ..., {x_{101}}$ such that ${x_1} < {x_2} < {x_3} < ... < {x_{100}} < {x_{101}}$. The mean deviation of this set of observations about a point $k$ is minimum when $k$ equals:
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View SolutionThe mean of a set of observations is $\bar{x}$. If each observation is divided by $\alpha$ $(\alpha \neq 0)$ and then increased by $10$,what is the mean of the new set?
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View SolutionThe mean of the first three terms is $14$ and the mean of the next two terms is $18$. What is the mean of all five terms?
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View SolutionThe median of a set of $9$ distinct observations is $20.5$. If each of the largest $4$ observations of the set is increased by $2$,then the median of the new set:
Find the arithmetic mean of the following frequency distribution.
$x_i$ $5$ $8$ $11$ $14$ $17$ $f_i$ $4$ $5$ $6$ $10$ $20$
| $x_i$ | $5$ | $8$ | $11$ | $14$ | $17$ |
| $f_i$ | $4$ | $5$ | $6$ | $10$ | $20$ |
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