Question

Find the mean of a, b, c if :

- mean of a,b is 25
- mean of b,c is 28
- mean of a,c is 22

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Answer 1

$\;\;\underline{\textbf{\textsf{ Given:-}}}$

• Mean of a and b is 25.

•Mean of b and c is 28.

•Mean of c and a is 22.

$\;\;\underline{\textbf{\textsf{ To Find :-}}}$

• What's the mean of a, b and c?

$\;\;\underline{\textbf{\textsf{ Formula Used :-}}}$

•Mean = $\bf \dfrac{Sum \: of \: observations}{No \: of \: observations}$

$\;\;\underline{\textbf{\textsf{ Solution :-}}}$

Given that,

•Mean of a and b is = 25

⟶ $\sf \dfrac{a+b}{2} = 25$

⟶ $\sf a + b = 25 × 2$

⟶ $\sf a + b = 50 \: \: \:...(i)$

________________________________________________

•Mean of b and c is 28.

⟶ $\sf \dfrac{b+c}{2} = 28$

⟶ $\sf b+c = 28 × 2$

⟶ $\sf b+c = 56 \: \: \:...(ii)$

_______________________________________________

•Mean of c and a is 22.

⟶ $\sf \dfrac{c+a}{2} = 22$

⟶ $\sf c + a= 22 × 2$

⟶ $\sf c+a = 44\: \: \:...(iii)$

$\:\:\:\:\dag\bf{\underline \green{Adding \:these\:equations :-}}$

⟶ $\sf a+b+b+c+c+a=50+56+44$

⟶ $\sf 2a + 2b + 2c =150$

⟶ $\sf 2(a+b+c)=150$

⟶ $\sf a + b + c = \dfrac{150}{2}$

⟶ $\sf a+b+c = 75$

_______________________________________________

Now,

•Mean of a, b and c = $\sf \dfrac{a+b+c}{3}$

= $\sf \dfrac{75}{3}$

= $\sf 25$

$\:\:\:\:\dag\bf{\underline{\underline \green{Hence:-}}}$

Mean of a, b, c is 25.