Question

the average of 10 numbers is 9.6,if the average od the first five is 9.4 and that of the last five is 10.5,the fifth number is​

Answer 1

The fifth number is 3.5

Given:

Average of 10 numbers = 9.6

Average of first 5 numbers = 9.4

Average of last five numbers = 10.5

To find:

The fifth number in the series.

Solution:

As we know average is where the sum of all the observations divided by the number of observations is included. Since we know averages as well as the no of observations, we can substitute to find out the sum of observations.

i. 10 numbers:

Average = Sum of observations / No of observations

9.6 = Sum of observations / 10

The sum of observations = 10 x 9.6

The sum of observations = 96

ii. First 5 numbers:

Average = Sum of observations / No of observations

9.4 = Sum of observations / 5

The sum of observations = 5 x 9.4

The sum of observations = 47

iii. Last 5 numbers:

Average = Sum of observations / No of observations

10.5 = Sum of observations / 5

The sum of observations = 5 x 10.5

The sum of observations = 52.5

Now let us find the fifth number. The fifth number would be the last number of the first five numbers and the first number of the last five numbers.

so,

Fifth number = ( Sum of first five numbers + Sum of last five numbers ) - ( Sum of ten numbers )

Fifth number = ( 47 + 52.5 ) - 96

Fifth number = 99.5 - 96

Fifth number = 3.5

Therefore, the fifth number is 3.5

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