Answers from page 2 onwards. In simple terms, explain what each of the following formulas are telling you to do a. ?? b. EX2 c. (EX)2 d. ?(X - 1) e. ?(? - 1)2 Apply the formulas above to each of the following datasets: i. 3, 5, 9, 3 ii. -3, -5, -9, -3 iii. 3, -5, 9, -3 iv. X f 0 1 1 2 2 1 3 4
Answers a. ?? The sum of raw scores b. EX2 The sum of the squared raw scores C. (??)2 The squared sum of raw scores d. E(X- 1) Raw scores have 1 subtracted from them and then they are summed e. ?(? - 1)2 The raw scores have 1 subtracted from them, then each is squared, and finally all summed. i. 3, 5, 9, 3 ??= 3+5+9+3 = 20 ??2 = 32 + 52 + 92 + 32 = 9+ 25 + 81 + 9 = 124 (??)2 = (3 + 5+9+3)2 = 202 = 400 ?(X - 1) = (3 - 1) + (5 - 1) + (9 - 1) + (3 - 1) =2+4+8+ 2 = 16 ?(X - 1)2 = (3 - 1)2 + (5 - 1)2 + (9 - 1)2 + (3-1)2 = 22 + 42 + 82 + 22 =4+ 16+ 64 + 4 = 88
ii. -3,-5,-9,-3 ??= - 3+-5+-9+-3 =- 3-5- 9-3 = - 20 ??2 = (-3)2 + (-5)2 + (-9)2 + (-3)2 = 9 + 25 + 81 + 9 = 124 (??)2 = (-3 - 5 - 9 - 3)2 = (-20)2 = 400 ?(X - 1) = (-3 - 1) + (-5 - 1) + (-9 - 1) + (-3 - 1) =- 4+-6+-10+-4 =- 4- 6 - 10 -4 =- 24 ?(? - 1)2 = (-3 - 1)2 + (-5 - 1)2 + (-9 - 1)2 + (-3 - 1)2 = (-4)2 + (-6)2 + (-10)2 + (-4)2 = 16 + 36 + 100 + 16 = 168