Question

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?

Answer 1

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