Question

average of 10,20,30,40, 50,60,70,80,90 and 100=​

Answer 1

Step-by-step explanation:

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Answer 2

The average of 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 and 100 is 55

Given :

The observations 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 and 100

To find :

The average of 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 and 100

Solution :

Step 1 of 2 :

Calculate Sum of the observations

Here the given observations are 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 and 100

Number of observations = 10

Sum of the observations

$\sf \: = 10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90 + 100$

$\displaystyle \sf{ = 10(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) }$

$\displaystyle \sf{ = 10 \times \frac{10(10 + 1)}{2} }$

$\displaystyle \sf{ = 10 \times \frac{10 \times 11}{2} }$

$\displaystyle \sf{ = 10 \times 5 \times 11 }$

$\sf = 550$

Step 2 of 2 :

Calculate the average

The required average

$\displaystyle \sf{ = \frac{Sum \: of \: the \: observations}{Number \: of \: observations} }$

$\displaystyle \sf{ = \frac{550}{10} }$

$\displaystyle \sf{ = 55}$

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