The average of 6 observations is 12. If the 7th observation is included, the average is reduced by 1. What will be the 7th observation?
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let observations are x₁ ,x₂,x₃,x₄, x₅ ,x₆
[x₁ +x₂+x₃+x₄+x₅+x₆ ]÷6=12
[x₁ +x₂+x₃+x₄+x₅+x₆ ]=72
[x₁ +x₂+x₃+x₄+x₅+x₆+x₇]÷7=12-1
[x₁ +x₂+x₃+x₄+x₅+x₆+x₇]=11*7
[x₁ +x₂+x₃+x₄+x₅+x₆+x₇ ]=77
[72+x₇]=77
x₇=77-72=5 which is 7th observation
[x₁ +x₂+x₃+x₄+x₅+x₆ ]÷6=12
[x₁ +x₂+x₃+x₄+x₅+x₆ ]=72
[x₁ +x₂+x₃+x₄+x₅+x₆+x₇]÷7=12-1
[x₁ +x₂+x₃+x₄+x₅+x₆+x₇]=11*7
[x₁ +x₂+x₃+x₄+x₅+x₆+x₇ ]=77
[72+x₇]=77
x₇=77-72=5 which is 7th observation
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