Question

STATEMENT - 1: The mean of the data set of $1000$ times is $5$. From each item $3$ is subtracted and then each number is multiplied by $2$. The new mean will be 4.
STATEMENT - 2 : The new mean $=$ [{old mean $\times$ no. of data set $-$ no. subtracted from each item $\times$ no. of data set } $\times$ multiple factor ]/no. of data set

• A. Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1
• B. Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1
• C. Statement - 1 is True, Statement - 2 is False
• D. Statement - 1 is False, Statement - 2 is True

Answer 1

The correct option is A Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1

Statement $1:$

The mean of data set of $1000$ times is $5$

$\therefore$ Sum of data set $=1000\times 5=5000$

Each item $3$ is subtracted and then each number is multiplied by $2$

$\therefore$ New sum of data $=[5000-(3\times 1000\left)\right]\times 2=4000$

$\therefore$ New mean $=\frac{4000}{1000}=4$

$\therefore$ Statement $1$ is true.

$\Rightarrow$ We can see, statement $2$ is a correct explanation for statement $1$

$\therefore$ Correct answer is option $A.$