Question

5. The means of 20 items of a data is 5 and if each item is multiplied by 3, then the new mean will be (b) 5 15 (d) 10​

Answer 1

Answer:

Given :-

• The means of 20 items of a data is 5 and if item is multiplied by 3.

To Find :-

• What is the new mean.

Formula Used :-

$\clubsuit$ Mean Formula :

$\small\mapsto \sf\boxed{\bold{\pink{Mean =\: \dfrac{Sum\: Of\: Observations}{Total\: Number\: Of\: Observations}}}}$

Solution :-

$\bigstar$ The mean of 20 items of a data is 5.

Hence, the sum of all 20 items is :

$\implies \sf 20 \times 5$

$\implies \sf\bold{\purple{100}}$

Again,

$\bigstar$ If each item is multiplied by 3.

Then, the new sum of all 20 items is :

$\implies \sf 3 \times 100$

$\implies \sf\bold{\purple{300}}$

Now, we have to find the new mean :

Given :

• Sum of Observations = 300
• Total Number Of Observations = 20

According to the question by using the formula we get,

$\small\longrightarrow \bf Mean =\: \dfrac{Sum\: Of\: Observations}{Total\: Number\: Of\: Observations}$

$\longrightarrow \sf Mean =\: \dfrac{30\cancel{0}}{2\cancel{0}}$

$\longrightarrow \sf Mean =\: \dfrac{\cancel{30}}{\cancel{2}}$

$\longrightarrow \sf Mean =\: \dfrac{15}{1}$

$\longrightarrow \sf\bold{\red{Mean =\: 15}}$

${\small{\bold{\underline{\therefore\: The\: new\: mean\: is\: 15\: .}}}}$

Hence, the correct options is option no (c) 15.