If the average of five observations $$a_1, a_2, a_3, a_4 and a_5$$ is N, then what is the average of five new observations $$a_1 - 100, a_2 - 100, a_3 - 100, a_4 - 100, and a_5 - 100$$?
Given, $$\dfrac{a_1+ a_2+ a_3+ a_4+ a_5}{5} = N$$
=> $$a_1+ a_2+ a_3+ a_4+ a_5 = 5N$$
Then, Average of $$a_1 - 100, a_2 - 100, a_3 - 100, a_4 - 100, and a_5 - 100$$ = $$\dfrac{a_1+ a_2+ a_3+ a_4+ a_5-500}{5} = \dfrac{5N-500}{5} = N-100$$
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