An instructor combines two exam results:

• Group 1: $n_1 = 40$ students, mean score = 78, SD = 6
• Group 2: $n_2 = 60$ students, mean score = 84, SD = 6

Which statement(s) is/are TRUE about the combined dataset? (Select all that apply)

I. The combined mean is $(78 + 84)/2 = 81$ II. The combined mean is $(40 \times 78 + 60 \times 84)/100 = 81.6$ III. The combined SD equals 6 (unchanged from both groups) IV. The combined SD is greater than 6 due to variation between the group means