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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Statistics

NDA 2018 · Mathematics · Statistics

Let x be the mean of x_1, x_2, x_3, , x_n . If x_i=a+cy_i for some...

Let xˉ\bar{x} be the mean of x1,x2,x3,…,xnx_1, x_2, x_3, \ldots, x_n. If xi=a+cyix_i=a+cy_i for some constants a and cc, then what will be the mean of y1,y2,y3,….,yn\mathrm{y}_1, \mathrm{y}_2, \mathrm{y}_3, \ldots., \mathrm{y}_{\mathrm{n}} ?

Options

  1. Aa+cxˉa+c \bar{x}
  2. Ba−1cxˉa-\frac{1}{c} \bar{x}
  3. C1cx‾−a\frac{1}{\mathrm{c}} \overline{\mathrm{x}}-\mathrm{a}
  4. Dxˉ−ac\frac{\bar{x}-a}{c}

Correct answer

D. xˉ−ac\frac{\bar{x}-a}{c}

Step-by-step solution

 Given, Mean of xi=x‾Also, Given xi=a+cyyi∴ Mean of a+cyi=x‾⇒ Mean of cyi=x‾−a⇒ Mean of yi=x‾−ac\begin{aligned} & \text{ Given, Mean of } \mathrm{x}_{\mathrm{i}}=\overline{\mathrm{x}} \\ & \text{Also, Given } \mathrm{x}_{\mathrm{i}}=\mathrm{a}+\mathrm{cy} \mathrm{y}_{\mathrm{i}} \\ & \therefore \quad \text{ Mean of } \mathrm{a}+\mathrm{cy}_{\mathrm{i}}=\overline{\mathrm{x}} \\ & \Rightarrow \text{ Mean of } \mathrm{cy}_{\mathrm{i}}=\overline{\mathrm{x}}-\mathrm{a} \\ & \Rightarrow \text{ Mean of } \mathrm{y}_{\mathrm{i}}=\frac{\overline{\mathrm{x}}-\mathrm{a}}{\mathrm{c}}\end{aligned}
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