There are 50 numbers. Each number is subtract | vedclass

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

Question

(B) Let the $50$ numbers be $x_1, x_2, \dots, x_{50}$ and their mean be $\bar{x}$.According to the problem, each number is subtracted from $53$, so th

Vedclass · Accepted Answer

$56$

Vedclass · Answer

(B) Let the $50$ numbers be $x_1, x_2, \dots, x_{50}$ and their mean be $\bar{x}$.According to the problem, each number is subtracted from $53$, so the new numbers are $(53 - x_1), (53 - x_2), \dots, (53 - x_{50})$.The mean of these new numbers is given as $-3.5$.$	ext{Mean} = \frac{\sum_{i=1}^{50} (53 - x_i)}{50} = -3.5$$\Rightarrow \frac{(53 	imes 50) - \sum_{i=1}^{50} x_i}{50} = -3.5$Since $\bar{x} = \frac{\sum x_i}{50}$, we have $\sum x_i = 50 \bar{x}$.Substituting this into the equation:$\Rightarrow \frac{2650 - 50 \bar{x}}{50} = -3.5$$\Rightarrow 53 - \bar{x} = -3.5$$\Rightarrow \bar{x} = 53 + 3.5 = 56.5$Thus, the mean of the given numbers is $56.5$.

There are $50$ numbers. Each number is subtracted from $53$ and the mean of the numbers so obtained is found to be $-3.5$. The mean of the given numbers is: (in $.5$)

Similar Questions

The mean of five numbers is $30$. If one number is excluded,their mean becomes $28$. The excluded number is:

In a frequency distribution,the mid value of a class is $10$ and the width of the class is $6$. The lower limit of the class is:

....... is a branch of Mathematics in which the extraction of meaningful information is studied.

The weights (in $kg$) of $11$ students are given below:
$37, 42, 40, 39, 41, 35, 37, 36, 40, 40, 42$
Find the median of the data.

State whether each of the following statements is true or false:
$(1)$ The median of the observations $12, 13, 14, 15, 16$ is $14$.
$(2)$ The mode of the observations $1, 3, 5, 7, 9$ is $5$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module