Question

if :

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

find the mean of a,b,c


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Answer 1

Answer:

$\underline{\boxed{\bf Mean \: of \: a, b \: and \: c = 25}}$

Step-by-step explanation:

Given that :

• Mean of a and b is 25.
• Mean of b and c is 28.
• Mean of c and a is 22.

To find :

• The mean of a, b and c.

Solution :

We know that,

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

CASE I :

Mean of a and b = 25.

⇒ $\sf \dfrac{a+b}{2} = 25$

⇒ $\sf a + b = 25 * 2$

⇒ $\sf a + b = 50 \: \: \:...(i)$

CASE II :

Mean of b and c is 28.

⇒ $\sf \dfrac{b+c}{2} = 28$

⇒ $\sf b+c = 28 * 2$

⇒ $\sf b+c = 56 \: \: \:...(ii)$

CASE III :

Mean of c and a is 22.

⇒ $\sf \dfrac{c+a}{2} = 22$

⇒ $\sf c + a= 22 * 2$

⇒ $\sf c+a = 44\: \: \:...(iii)$

Adding equation (i), (ii) and (iii) -

⇒ $\sf a+b+b+c+c+a=50+56+44$

⇒ $\sf 2a + 2b + 2c =150$

⇒ $\sf 2(a+b+c)=150$

⇒ $\sf a + b + c = \dfrac{150}{2}$

⇒ $\sf a+b+c = 75$

Now,

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

⇒ Mean of a, b and c = $\sf \dfrac{75}{3}$

⇒ Mean of a, b and c = $\sf 25$

Hence, the answer is 25.

Answer 2

Answer:

$\large\boxed{\sf{25}}$

Step-by-step explanation:

Given that,

Mean of a, b is 25

Therefore, we get,

$= > \dfrac{a + b}{2} = 25 \\ \\ = > a + b = 25 \times 2 \\ \\ = > a + b = 50 \: \: \: \: .......(1)$

Mean of b, c is 28

Therefore, we get,

$= \dfrac{b + c}{2} = 28 \\ \\ = > b + c = 28 \times 2 \\ \\ = > b + c = 56 \: \: \: \: .......(2)$

Mean of a, c is 22

Therefore, we will get,

$= > \dfrac{a + c}{2} = 22 \\ \\ = > a + c = 22 \times 2 \\ \\ = > a + c = 44 \: \: \: \: .......(3)$

Adding eqn (1), (2) and (3), we get,

$= > 2(a + b + c) = 50 + 56 + 44 \\ \\ = > 2(a + b + c) = 150 \\ \\ = > a + b + c = \dfrac{150}{2} \\ \\ = > a + b + c = 75$

Now, to find the mean of a, b and c.

We know that,

Mean = Sum of digits/No. of digits

Therefore, we will get,

=> Mean = (a+b+c)/3

=> Mean = 75/3

=> Mean = 25

Hence, required mean is 25.