Question

9. The average of 11 results is 30 that of the
first 5 is 25 and that of the last 5 is 28. The
value of the 6th number is
(1) 64
(3) 66
(4) 45
(2) 65​

Answer 1

Answer:

Mean, median and mode are the representative values of a ... The range of the data 14, 6, 12, 17, 21, 10, 4, 3 is ... [Hint : First five prime numbers are 2, 3, 5, 7 and 11].

35 pages·1 MB

Answer 2

$\begin{gathered} \begin{gathered}\begin{gathered}\\\;\underbrace{\underline{\sf{Given \; Question:-}}}\end{gathered}\end{gathered} \end{gathered}$

The average of 11 results is 30 that of the first 5 is 25 and that of the last 5 is 28. The value of the 6th number is

Let's do it !!

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★ Formula Used :-

$\begin{gathered}\\\;\boxed{\sf{\pink{average = \frac{sum \: of \: all \: observation}{number \: of \: observation} }}}\end{gathered}$

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★ Solution :-

Given ,

• The average of 11 numbers is 30

• The average of first five number is 25

• The average of last five number is 28

To find ,

• The value of 6th observation

so we can find the value of 6 observation by adding the the sum of first five numbers from the sum of last five numbers and then subtracting them from the sum of 11 numbers

→ Sum of 11 numbers - ( Sum of first 5 no. + sum of last 5 no. )

Now , let's find the

• sum of 11 observation

• sum of first 5 observation

• sum of last 5 observations

we will find the sum of observations by applying the formula of average.

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Sum of 11 observations

It is given that the average of 11 result in 30

$\begin{gathered}\\\;\boxed{\sf{\pink{average = \frac{sum \: of \: all \: observations}{number \: of \: observations} }}}\end{gathered}$

$\begin{gathered}\\\; \Longrightarrow{\sf{{30= \frac{sum \: of \: 11 \: observations}{11} }}}\end{gathered}$

$\begin{gathered}\\\; \Longrightarrow{\sf{{sum \: of \: 11 \: observations= 30 \times 11 }}}\end{gathered}$

$\begin{gathered}\\\; \Longrightarrow{\sf{{sum \: of \: 11 \: observations= \blue{330}}}}\end{gathered}$

Sum of first 5 observations

It is given that the average of first 5 result in 25

$\begin{gathered}\\\;\boxed{\sf{\pink{average = \frac{sum \: of \: all \: observations}{number \: of \: observations} }}}\end{gathered}$

$\begin{gathered}\\\; \Longrightarrow{\sf{{25= \frac{sum \: of \: 5 \: observations}{5} }}}\end{gathered}$

$\begin{gathered}\\\; \Longrightarrow{\sf{{sum \: of \: 5 \: observations= 25 \times 5 }}}\end{gathered}$

$\begin{gathered}\\\; \Longrightarrow{\sf{{sum \: of \: first \: 5 \: observations= \blue{125}}}}\end{gathered}$

Sum of last 5 observations

It is given that the average of last 5 result in 28

$\begin{gathered}\\\;\boxed{\sf{\pink{average = \frac{sum \: of \: all \: observations}{number \: of \: observations} }}}\end{gathered}$

$\begin{gathered}\\\; \Longrightarrow{\sf{{28= \frac{sum \: of \: 5 \: observations}{5} }}}\end{gathered}$

$\begin{gathered}\\\; \Longrightarrow{\sf{{sum \: of \: 5 \: observations= 28 \times 5 }}}\end{gathered}$

$\begin{gathered}\\\; \Longrightarrow{\sf{{sum \: of \: last \: 5 \: observations= \blue{140}}}}\end{gathered}$

Now we know that

we can find the value of 6 observation by adding the the sum of first five numbers from the sum of last five numbers and then subtracting them from the sum of 11 numbers

→ Sum of 11 numbers - ( Sum of first 5 no. + sum of last 5 no. )

→ 330 - ( 125 + 140 )

→ 330 - 265

→ 65

$\: \: \boxed{\boxed{\bf{\mapsto \: \: \: hence , The \; value \: of \: 6 \: observation= \blue{\underline{(2) \;65}}}}}$