The mean of 5 numbers is 25. If one no is excluded the new mean is 24. find the excluded no
Answers
Answer:
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Step-by-step explanation:
Mean is the sum of the numbers divided by the total number of values.
Given that the arithmetic mean of 5 numbers is 27.
Let the numbers be x
1
,x
2
,x
3
,x
4
,x
5
Therefore, 27=
5
x
1
+x
2
+x
3
+x
4
+x
5
x
1
+x
2
+x
3
+x
4
+x
5
=27×5=135 -------(1)
After excluding one number then the mean is 25
Let the excluded number be x
5
Therefore, 25=
4
x
1
+x
2
+x
3
+x
4
x
1
+x
2
+x
3
+x
4
=25×4=100 ------(2)
subtracting (1) and (2) we get
(x
1
+x
2
+x
3
+x
4
+x
5
)−(x
1
+x
2
+x
3
+x
4
)=135−100
⟹x
5
=35
Therefore, the excluded number is 35
⍟ Mean of 5 numbers = 25
Sum of 5 numbers = 5 × 25 = 125
⍟ Mean of 4 numbers = 24
Sum of 4 numbers = 96
______________________________
⍟ Therefore, 5th number = 125 - 96 = 29