Question

The mean of 7 observation is 2,3,7,10,a,b,c is 7 find the mean of a,b,c

Answer 1

Answer:

The required mean is 9.

Step-by-step-explanation:

We have given that,

The mean of the 7 observations 2, 3, 7, 10, a, b, c is 7.

We have to find the mean of a, b, c.

Now, we know that,

$\displaystyle{\pink{\sf\:Mean\:=\:\dfrac{Sum\:of\:observations}{No.\:of\:observations}}}$

$\displaystyle{\implies\sf\:7\:=\:\dfrac{2\:+\:3\:+\:7\:+\:10\:+\:a\:+\:b\:+\:c}{7}}$

$\displaystyle{\implies\sf\:2\:+\:3\:+\:7\:+\:10\:+\:a\:+\:b\:+\:c\:=\:7\:\times\:7}$

$\displaystyle{\implies\sf\:2\:+\:10\:+\:10\:+\:a\:+\:b\:+\:c\:=\:49}$

$\displaystyle{\implies\sf\:2\:+\:20\:+\:a\:+\:b\:+\:c\:=\:49}$

$\displaystyle{\implies\sf\:22\:+\:a\:+\:b\:+\:c\:=\:49}$

$\displaystyle{\implies\sf\:a\:+\:b\:+\:c\:=\:49\:-\:22}$

$\displaystyle{\implies\sf\:a\:+\:b\:+\:c\:=\:27}$

Now,

$\displaystyle{\sf\:Mean\:=\:\dfrac{a\:+\:b\:+\:c}{3}}$

$\displaystyle{\implies\sf\:Mean\:=\:\cancel{\dfrac{27}{3}}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:Mean\:=\:9\:}}}}$

∴ The required mean is 9.

Answer 2

Question :-

The mean of 7 observation is 2,3,7,10,a,b,c is 7 find the mean of a,b,c.

Answer :-

• Mean of a, b, c is 9.

Step by step explanation :-

Here, we find the first values of a, b, c then we'll find the mean.

We know that,

$\sf\implies{Mean = \frac{Sum \: of \: all \: observations }{No. \: of \: all \: observations}}$

Now,

$\sf\implies{7 = \frac{2 + 3 + 7 + 10 + a + b + c}{7} } \\ \\ \sf\implies{7 \times 7 = 22 + a + b + c } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf\implies{ 49 - 22 = a + b + c} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf\implies \red{ a + b + c = 27} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Now, we find the mean of a, b, c.

$\sf\implies{ \frac{a + b + c}{3} } \: \: \: \: \\ \\ \sf\implies{ \frac{27}{3} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf\implies \red{mean = 9 }$

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