Question

the mean of 5 numbers is 27 if one number is excluded there mean is 25 find the excluded observation

Answer 1

given that, the mean of 5 no. = 27
let, those numbers are n1, n2, n3, n4, n5

so,
n1+ n2+ n3+ n4 + n5
_________________= 27
5

=> n1 + n2+ n3+ n4+ n5 = 27×5
=> n1 + n2+ n3 + n4 + n5 = 135 ___(1)

if one observation is excluded, say n5
so the new mean will be

n1+ n2 +n3 +n4
____________ = 25
4

=> n1+ n2+ n3 +n4 = 25× 4
=> n1+ n2 + n3 + n4= 100. ____(2)

eq. (1) - eq(2)

n1+n2+n3+n4+n5-(n1+n2+n3+n4)= 135 - 100

=> n1+n2+n3+n4+n5-n1-n2-n3-n4 = 35

=> n5 = 35

Answer 2

hi friends,

the solution of the answer is given below

given that, the mean of 5 no. = 27

let, those numbers are n1, n2, n3, n4, n5

so,

n1+ n2+ n3+ n4 + n5

_________________= 27

5

=> n1 + n2+ n3+ n4+ n5 = 27×5

=> n1 + n2+ n3 + n4 + n5 = 135 ___(1)

if one observation is excluded, say n5

so the new mean will be

n1+ n2 +n3 +n4

____________ = 25

4

=> n1+ n2+ n3 +n4 = 25× 4

=> n1+ n2 + n3 + n4= 100. ____(2)

eq. (1) - eq(2)

n1+n2+n3+n4+n5-(n1+n2+n3+n4)= 135 - 100

=> n1+n2+n3+n4+n5-n1-n2-n3-n4 = 35

=> n5 = 35