Arithmetic mean Formula:

Question

Arithmetic mean= a1 + a2 + a3...an⁄n 

 

How is this = 1⁄n ∑ ai , i=1  ? (How i=1?)

Answer 1

You should write  arithmetic mean = (a₁+a₂+…+a_n) / n    (use parenthesis to make your equation correct, this will also help you keep things straight)

 

What is (a₁+a₂+…+a_n )?     it is  ∑(a_i)  taken over  i=1…n,  no?   The i subscript just serves as an index to your different data values, i=1 for the first one (a₁),  i=2 for the 2nd one (a₂), etc., up to the n^th one (a_n).     The sigma notation ends up being more compact and easier to deal with in working out problems.   Multiplying by (1/n) out in front just divides the sum by n, which is the arithmetic mean you started with at the beginning, so the two are equivalent.