Question

The mean of
The mean of x1, x2 is 6, and x1, x2, x3 is 7. find the value of x3

Answer 1

Question :-

The mean of $\rm{x_{1},x_{2} }$ is 6 and $\rm{x_{1} ,x_{2} ,x_{3} }$ is 7. Find the value of $\rm{x_{3} ,}$ .

Answer :-

• $\rm{x_{3} =9 }$

Step by step explanation :-

We know that,

$\rm:\longmapsto{mean = \frac{sum \: of \: all \: observations}{total \: number \: of \: observations} }$

On the given information first we take the mean of x1 and x2 find his some then substitute the sum of value x1 and x2.

$\rm:\longmapsto{ \frac{x_{1} + {x_{2}}}{2} = 6} \: \: \: \: \: \\ \\ \rm:\longmapsto{{x_{1} + {x_{2}}} = 6 \times 2} \\ \\ \bf:\longmapsto \red{{x_{1} + {x_{2}}} =12} \: \: \:$

Substituting x1 + x2 = 12 in second mean.

$\rm:\longmapsto{ \frac{{x_{1} + {x_{2}}} +x_{3} }{3} = 7} \: \: \: \: \: \: \: \\ \\ \rm:\longmapsto{ {x_{1} + {x_{2}}} +x_{3} = 7 \times 3} \\ \\ \rm:\longmapsto{12+x_{3} = 21} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \rm:\longmapsto{x_{3} = 21 - 12} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf:\longmapsto \red{x_{3} = 9} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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