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The mean of 5 number is 18. If one number is excluded, their mean is 16. Find the excluded number

Mean = 5

Total no. of numbers = 18

Sum of all numbers = mean X no. of numbers = 5 X 18 = 90

Let excluded no. be x

Then, 90 - x / 4 = 16

= 90 - x = 16 X 4 = 64

= -x = 64 - 90 = - 26

= x = -26 / -1

= 26

Therefore, excluded number is 26.

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Mean = 18

total no. of obserxations = 5

mean = sum of observations / no. of observations

18 = sum / 5

sum of observations = 18 X 5 = 90

Now, after the exclusion of number, we have 

mean = 16

total no. of observations = 4

mean = sum of 4 ob. / no. of ob.

16 = sum / 4

sum of these 4 ob. = 16 X 4= 64

So, 

the excluded number = previous sum - new sum = 90 - 64 = 26

 

so, the excluded no is 26

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Let the original mean of five number be x.

Mean= Sum of numbers/Number of numbers

=> 18=x/5

=> 18*5=x

=>90=x

Therefore sum of numbers is 90.

Now, Modified mean=16

Let this mean be 'a'

a/4=16

=> a=64

Therefore Sum of numbers now is equal to 64

Now, the excluded number equal difference of Modified mean from Original mean

That is,

x-a=90-64=26

Required Answer--->Therefore the excluded number is 26

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