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$If the arithmetic mean of the numbers x_{1}, x_{2}, x_{3}, \dots, x_{n} is \bar{x}, then the arithmetic mean of the numbers a x_{1} + b, a x_{2} + b, a x_{3} + b, \dots, a x_{n} + b, where a, b are two constants, would be$

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Correct option is D

Required Mean=ax1+b+ax2+b+⋯+axn+bn=ax1+x2+⋯+xnn+b=ax¯+b∵x1+x2+⋯+xnn=x¯

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Variate x	1	2	3	4	5
Frequency f of x	4	5	y	1	2

If the arithmetic mean of the numbers x1,x2,x3,…,xn is x¯ , then the arithmetic mean of the numbers ax1+b,ax2+b , ax3+b,…,axn+b, where a,b are two constants, would be

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$If the arithmetic mean of the numbers x_{1}, x_{2}, x_{3}, \dots, x_{n} is \bar{x}, then the arithmetic mean of the numbers a x_{1} + b, a x_{2} + b, a x_{3} + b, \dots, a x_{n} + b, where a, b are two constants, would be$