The mean of eight numbers is 23. One more number is added to it. The new mean is reduced to 22. Find the number added.

Answers 2

Step-by-step explanation:

the answer is in the photo

Answer:

The required number is 14

Step-by-step explanation:

In simple words, the mean means average which is calculated by the sum of all the values divided by the number of values

Given that the mean of eight numbers is 23 and on the addition of the 9th number, the mean is reduced to 22 and we are supposed to find that the 9th number

Step 1:

Let eight numbers be a,b,c,d,e,f,g,h
Since the mean of eight numbers is 23 so that means according to the formula of mean we have

[tex]\frac{a+b+c+d+e+f+g+h}{8}=23[/tex]

Step 2:

Now obtain the value of a+b+c+d+e+f+g+h by multiplying 8 in the denominator to 23 on right-hand side.

We get

[tex]{a+b+c+d+e+f+g+h}=23*8[/tex]

[tex]{a+b+c+d+e+f+g+h}=184[/tex] -(1)

Step 3:

[tex]\frac{a+b+c+d+e+f+g+h+x}{9}=22[/tex]

Step 4:

Now obtain the value of a+b+c+d+e+f+g+h+x by multiplying 9 in denominator to 22 in right hand side.

We get

[tex]{a+b+c+d+e+f+g+h+x}=198[/tex] -(2)

Step 5:

Now substitute the value of a+b+c+d+e+f+g+h from (1) into (2)

We get

184+x=198

On simplification we get

x=14

Therefore the required number that was added was 14