Question

nine trends are standing in height order from the smallest on the left and tallest on the right the 5 trends from the left have an average height of 150 cm. the 5 trends from the right have an average height of 170cm. if the middle trend who is 160cm tall leaves then what is the average height of the remaining 8 trends?​

Answer 1

Answer:

160

Step-by-step explanation:

9 friends : a,b,c,d,e,f,g,h,i

let assume a is on the left and i is on the right side.

So, (a+b+c+d+e)/5 =150  (Given)

and (e+f+g+h+i)/5= 170 (Given)

and e= 160

hence, a+b+c+d+160 = 150*5  

a+b+c+d=750-160 = 590

Similarly,

160+f+g+h+i=170*5

f+g+h+i=850-160=690

Average of remaining 8 firend: ( (a+b+c+d)+(f+g+h+i)) /8

=> (590+690)/8 => 1280/8 => 160

Answer 2

Given: Nine trends are standing in height order from the smallest on the left and tallest on the right the 5 trends from the left have an average height of 150 cm. the 5 trends from the right have an average height of 170cm. The middle trend who is 160cm tall leaves.

To find: The average height of the remaining 8 trends.

Solution:

The average of a given set of values is given by dividing the sum of the values by the number of values. So, the average height of the 5 trends from the left and the 5 trends from the right can be written as follows.

$\frac{S_{1}}{5} = 150$

$S_{1} = 150 * 5$

$\frac{S_{2}}{5} = 170$

$S_{2} = 170 * 5$

Here, S₁ and S₂ are the sums of the heights of the 5 trends from the left and from the right, respectively. Now, when the middle trend of height 160 cm leaves, the given averages can be written as follows.

$S_{1} - 160 = (150*5) - 160$

$S_{2} - 160 = (170*5) - 160$

Now, the (S₁-160) represents the sum of the four trends from the left and (S₂-160) represents the sum of the four trends from the right. That makes a total of the remaining 8 trends. Thus, the average can be calculated as

$\frac{(150*5) - 160 + (170*5) - 160}{8} = \frac{1600 - 320}{8}$

                                   $= \frac{1280}{8}$

                                   $= 160 cm$

Therefore, the average height of the remaining 8 trends is 160 cm.