Question

Please explain these​

Answer 1

Answer:

Given :-

The mean of ten numbers is 58.

One of the numbers is 40.

To Find :-

What is the mean of other nine.

Formula Used :-

\begin{gathered} \longmapsto \sf\boxed{\bold{\pink{Mean =\: \dfrac{Sum\: of\: Observations}{Total\: number\: of\: Observations}}}}\\\end{gathered}

⟼

Mean=

TotalnumberofObservations

SumofObservations

Solution :-

\mapsto↦ The mean of ten numbers is 58, it means :

Mean = 58

Total number of observations = 10

According to the question by using the formula we get,

\begin{gathered} \implies \sf 58 =\: \dfrac{Sum\: of\: observations}{10}\\\end{gathered}

⟹58=

10

Sumofobservations

By doing cross multiplication we get,

\begin{gathered} \implies \sf Sum\: of\: observations =\: 10 \times 58\\\end{gathered}

⟹Sumofobservations=10×58

\begin{gathered} \implies \sf\bold{\green{Sum\: of\: observations =\: 580}}\\\end{gathered}

⟹Sumofobservations=580

Hence, the sum of observations is 580.

Again,

\mapsto↦ One of the numbers is 40,

Then,

\begin{gathered} \implies \sf Sum\: of\: observations =\: 580 -\: 40\\\end{gathered}

⟹Sumofobservations=580−40

\begin{gathered} \implies \sf\bold{\purple{Sum\: of\: observations =\: 540}}\\\end{gathered}

⟹Sumofobservations=540

Now, we have to find the mean of the other nine :

Given :

Sum of observations = 540

Total number of observations = 9

According to the question by using the formula we get,

\begin{gathered} \implies \sf Mean\: of\: other\: nine =\: \dfrac{\cancel{540}}{\cancel{9}}\\\end{gathered}

⟹Meanofothernine=

9

540

\begin{gathered} \implies \sf\bold{\red{Mean\: of\: other\: nine =\: 60}}\\\end{gathered}

⟹Meanofothernine=60

\therefore∴ The mean of other nine is 60.