The arithmetic mean of a set of observations | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $x_1, x_2, \dots, x_n$ be $n$ observations,then the mean is given by $\bar{X} = \frac{1}{n} \sum_{i=1}^{n} x_i$.Let the new observations be $y

Vedclass · Accepted Answer

$\frac{\bar{X} + 10\alpha}{\alpha}$

Vedclass · Answer

(C) Let $x_1, x_2, \dots, x_n$ be $n$ observations,then the mean is given by $\bar{X} = \frac{1}{n} \sum_{i=1}^{n} x_i$.Let the new observations be $y_i = \frac{x_i}{\alpha} + 10$.The mean of the new series $\bar{Y}$ is given by:$\bar{Y} = \frac{1}{n} \sum_{i=1}^{n} \left( \frac{x_i}{\alpha} + 10 \right)$$\bar{Y} = \frac{1}{\alpha} \left( \frac{1}{n} \sum_{i=1}^{n} x_i \right) + \frac{1}{n} (10n)$$\bar{Y} = \frac{\bar{X}}{\alpha} + 10$$\bar{Y} = \frac{\bar{X} + 10\alpha}{\alpha}$

The arithmetic mean of a set of observations is $\bar{X}$. If each observation is divided by $\alpha$ and then increased by $10$,then the mean of the new series is:

Similar Questions

The dispersive powers of the materials of two lenses forming an achromatic combination are in the ratio of $4: 3$. If the effective focal length of the two lenses is $+60 ~cm$,then the focal lengths of the lenses should be:

What is the path difference for destructive interference?

Three charges $2q, -q$ and $-q$ are located at the vertices of an equilateral triangle. At the centre of the triangle,

The equation of the pair of lines passing through the origin whose sum and product of slopes are respectively the arithmetic mean and geometric mean of $4$ and $9$ is

In a compound,$C, H,$ and $N$ atoms are present in the ratio $9 : 1 : 3.5$ by weight. If the molecular weight of the compound is $108$,what is its molecular formula?

Vedclass Test Series

Exam Paper Generator

Online Exam Module