The mean of 6 Observations is 20. On removing one number from the given set, the mean of the remaining numbers becomes 16. find the value of the removed number.
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Step-by-step explanation:
Given that mean of 6 numbers is 16
Let the numbers be a
1
,a
2
,a
3
,a
4
,a
5
,a
6
Therefore the mean =
6
a
1
+a
2
+a
3
+a
4
+a
5
+a
6
=16
⟹a
1
+a
2
+a
3
+a
4
+a
5
+a
6
=16×6=96 ....(1)
Let the removed number be a
6
Given that mean of the remaining numbers is 17
Therefore the mean =
5
a
1
+a
2
+a
3
+a
4
+a
5
=17
⟹a
1
+a
2
+a
3
+a
4
+a
5
=17×5=85 ....(2)
Substituting (2) in (1) we get
85+a
6
=96⟹a
6
=96−85=11
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